AP Precalculus Flashcards: Transformations Of Functions

Study Transformations Of Functions in AP Precalculus with focused flashcards that help you recognize the idea, recall the key rule, and apply it in practice-style prompts.

AP Precalculus

Transformations Of Functions

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QUESTION

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Identify the transformation: $f(x) = \frac{1}{x}$ to $f(x) = \frac{1}{-x}$

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ANSWER

Reflection across the y-axis. Negative input creates horizontal reflection.

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What this deck covers

This deck focuses on Transformations Of Functions, giving you a quick way to review the definitions, rules, and examples that matter most for AP Precalculus.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

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Flashcard 1: Identify the transformation: $f(x) = \frac{1}{x}$ to $f(x) = \frac{1}{-x}$

Answer: Reflection across the y-axis. Negative input creates horizontal reflection.

Flashcard 2: What is the effect of $cf(x)$ where $0 < c < 1$ ?

Answer: Vertical compression by a factor of $c$ . Multiplying by factor less than 1 compresses vertically.

Flashcard 3: Identify the transformation: $f(x) = |x|$ to $f(x) = 2|x|$

Answer: Vertical stretch by a factor of 2. Coefficient 2 multiplies all $y$ -values by 2.

Flashcard 4: What is the effect of $f(x)$ to $f(x + c)$ on its domain?

Answer: Subtract $c$ from each element of the domain. Horizontal shift adjusts input values by constant.

Flashcard 5: Identify the transformation: $f(x) = e^x$ to $f(x) = e^{-x}$

Answer: Reflection across the y-axis. Negative exponent reflects exponential across $y$ -axis.

Flashcard 6: What transformation does $-f(x)$ represent?

Answer: Reflection across the x-axis. Negative sign flips graph over the horizontal axis.

Flashcard 7: What is the effect of $cf(x)$ where $c > 1$ ?

Answer: Vertical stretch by a factor of $c$ . Multiplying by factor greater than 1 stretches vertically.

Flashcard 8: Identify the transformation: $f(x) = x^3$ to $f(x) = x^3 - 2$

Answer: Vertical shift downward by 2 units. Subtracting 2 from output moves graph down.

Flashcard 9: Identify the transformation: $f(x) = \frac{1}{x}$ to $f(x) = \frac{1}{x} + 1$

Answer: Vertical shift upward by 1 unit. Adding 1 to function output shifts graph upward.

Flashcard 10: What transformation is applied: $f(x) = \frac{1}{x}$ to $f(x) = \frac{1}{(x-4)}$ ?

Answer: Horizontal shift right by 4 units. Subtracting 4 from input shifts right by 4.

Flashcard 11: Identify the transformation: $f(x) = \frac{1}{x}$ to $f(x) = \frac{1}{x} - 5$

Answer: Vertical shift downward by 5 units. Subtracting 5 from output moves graph downward.

Flashcard 12: What is the effect of $f(x - c)$ on the graph of $f(x)$ ?

Answer: Horizontal shift right by $c$ units. Subtracting from input moves graph in same direction horizontally.

Flashcard 13: What is the effect of $f(x)$ to $f(-x)$ on its domain?

Answer: Negate each element of the domain. Reflection changes signs of all input values.

Flashcard 14: Identify the transformation: $f(x) = \frac{1}{x}$ to $f(x) = \frac{1}{x} + 7$

Answer: Vertical shift upward by 7 units. Adding 7 to function output shifts upward.

Flashcard 15: What is the effect of $cf(x)$ where $0 < c < 1$ ?

Answer: Vertical compression by a factor of $c$ . Multiplying by factor less than 1 compresses vertically.

Flashcard 16: What is the effect of $f(x) - c$ on the graph of $f(x)$ ?

Answer: Vertical shift downward by $c$ units. Subtracting constant from function output moves graph down.

Flashcard 17: What is the combined effect of $-f(x + 2)$ ?

Answer: Reflection across x-axis and left shift by 2. Combines vertical reflection and horizontal translation.

Flashcard 18: Identify the transformation: $f(x) = |x|$ to $f(x) = |x + 2|$

Answer: Horizontal shift left by 2 units. Adding 2 to input shifts left by 2 units.

Flashcard 19: What is the effect of $cf(x)$ where $c > 1$ ?

Answer: Vertical stretch by a factor of $c$ . Multiplying by factor greater than 1 stretches vertically.

Flashcard 20: Identify the transformation: $f(x) = \frac{1}{x}$ to $f(x) = \frac{1}{x} - 3$

Answer: Vertical shift downward by 3 units. Subtracting 3 from function output shifts downward.

Flashcard 21: What transformation does $f(-x)$ represent?

Answer: Reflection across the y-axis. Negative input creates mirror image across vertical axis.

Flashcard 22: Identify the transformation: $f(x) = x^2$ to $f(x) = x^2 + 5$

Answer: Vertical shift upward by 5 units. Adding 5 to function output shifts graph upward.

Flashcard 23: Identify the transformation: $f(x) = |x|$ to $f(x) = |x - 1|$

Answer: Horizontal shift right by 1 unit. Subtracting 1 from input shifts right by 1.

Flashcard 24: What transformation does $f(x) = x^2$ to $f(x) = -x^2$ represent?

Answer: Reflection across the x-axis. Negative sign flips parabola across $x$ -axis.

Flashcard 25: What transformation is applied: $f(x) = \frac{1}{x}$ to $f(x) = \frac{1}{(x-4)}$ ?

Answer: Horizontal shift right by 4 units. Subtracting 4 from input shifts right by 4.

Flashcard 26: Identify the transformation: $f(x) = \frac{1}{x}$ to $f(x) = \frac{1}{x} + 1$

Answer: Vertical shift upward by 1 unit. Adding 1 to function output shifts graph upward.

Flashcard 27: Identify the transformation: $f(x) = |x|$ to $f(x) = 3|x|$

Answer: Vertical stretch by a factor of 3. Factor 3 multiplies all $y$ -values by 3.

Flashcard 28: What is the effect of $f(x)$ to $-f(x)$ on its range?

Answer: Negate each element of the range. Reflection flips signs of all output values.

Flashcard 29: What transformation does $f(x) = x^2$ to $f(x) = (x + 5)^2$ represent?

Answer: Horizontal shift left by 5 units. Adding 5 to input shifts left by 5 units.

Flashcard 30: Identify the transformation: $f(x) = \frac{1}{x}$ to $f(x) = \frac{1}{x} - 5$

Answer: Vertical shift downward by 5 units. Subtracting 5 from output moves graph downward.

Flashcard 31: Identify the transformation: $f(x) = x^2$ to $f(x) = (x - 3)^2$

Answer: Horizontal shift right by 3 units. Inside parentheses: subtract 3 from $x$ shifts right.

Flashcard 32: Identify the transformation: $f(x) = x^3$ to $f(x) = x^3 - 2$

Answer: Vertical shift downward by 2 units. Subtracting 2 from output moves graph down.

Flashcard 33: What is the effect of $f(cx)$ where $c > 1$ ?

Answer: Horizontal compression by a factor of $\frac{1}{c}$ . Input coefficient greater than 1 compresses horizontally.

Flashcard 34: What is the effect of $f(x)$ to $-f(x)$ on its range?

Answer: Negate each element of the range. Reflection flips signs of all output values.

Flashcard 35: What is the effect of $f(x)$ to $cf(x)$ where $c < 0$ ?

Answer: Vertical stretch/compression and reflection across x-axis. Negative coefficient reflects and scales vertically.

Flashcard 36: Identify the transformation: $f(x) = \frac{1}{x}$ to $f(x) = \frac{1}{x} - 3$

Answer: Vertical shift downward by 3 units. Subtracting 3 from function output shifts downward.

Flashcard 37: Identify the transformation: $f(x) = x^3$ to $f(x) = (x + 4)^3$

Answer: Horizontal shift left by 4 units. Adding 4 to input moves graph left by 4.

Flashcard 38: Identify the transformation: $f(x) = \frac{1}{x}$ to $f(x) = \frac{1}{x+2}$

Answer: Horizontal shift left by 2 units. Adding 2 to input shifts graph left by 2.

Flashcard 39: What is the effect of $f(cx)$ where $0 < c < 1$ ?

Answer: Horizontal stretch by a factor of $\frac{1}{c}$ . Input coefficient less than 1 stretches horizontally.

Flashcard 40: What is the effect of $f(x + c)$ on the graph of $f(x)$ ?

Answer: Horizontal shift left by $c$ units. Adding to input moves graph opposite direction horizontally.

Flashcard 41: Identify the transformation: $f(x) = x^3$ to $f(x) = (x + 4)^3$

Answer: Horizontal shift left by 4 units. Adding 4 to input moves graph left by 4.

Flashcard 42: What is the effect of $f(x + c)$ on the graph of $f(x)$ ?

Answer: Horizontal shift left by $c$ units. Adding to input moves graph opposite direction horizontally.

Flashcard 43: What is the effect of $f(x)$ to $cf(x)$ where $c < 0$ ?

Answer: Vertical stretch/compression and reflection across x-axis. Negative coefficient reflects and scales vertically.

Flashcard 44: What is the effect of $f(x)$ to $f(x) + c$ on its range?

Answer: Add $c$ to each element of the range. Vertical shift adds constant to all output values.

Flashcard 45: What transformation does $f(x) = x^2$ to $f(x) = (x - 6)^2$ represent?

Answer: Horizontal shift right by 6 units. Subtracting 6 from input shifts right by 6.

Flashcard 46: What is the effect of $f(x)$ to $f(-x)$ on its domain?

Answer: Negate each element of the domain. Reflection changes signs of all input values.

Flashcard 47: Identify the transformation: $f(x) = \frac{1}{x}$ to $f(x) = \frac{1}{-x}$

Answer: Reflection across the y-axis. Negative input creates horizontal reflection.

Flashcard 48: What is the effect of $f(x - c)$ on the graph of $f(x)$ ?

Answer: Horizontal shift right by $c$ units. Subtracting from input moves graph in same direction horizontally.

Flashcard 49: Identify the transformation: $f(x) = x^2$ to $f(x) = (x - 3)^2$

Answer: Horizontal shift right by 3 units. Inside parentheses: subtract 3 from $x$ shifts right.

Flashcard 50: Identify the transformation: $f(x) = \frac{1}{x}$ to $f(x) = \frac{1}{x} + 7$

Answer: Vertical shift upward by 7 units. Adding 7 to function output shifts upward.

Flashcard 51: Identify the transformation: $f(x) = |x|$ to $f(x) = |x - 1|$

Answer: Horizontal shift right by 1 unit. Subtracting 1 from input shifts right by 1.

Flashcard 52: What transformation does $f(-x)$ represent?

Answer: Reflection across the y-axis. Negative input creates mirror image across vertical axis.

Flashcard 53: Identify the transformation: $f(x) = |x|$ to $f(x) = |x + 2|$

Answer: Horizontal shift left by 2 units. Adding 2 to input shifts left by 2 units.

Flashcard 54: What transformation does $f(x) = x^2$ to $f(x) = -x^2$ represent?

Answer: Reflection across the x-axis. Negative sign flips parabola across $x$ -axis.

Flashcard 55: What is the effect of $f(x) + c$ on the graph of $f(x)$ ?

Answer: Vertical shift upward by $c$ units. Adding constant to function output moves graph up.

Flashcard 56: What is the effect of $f(cx)$ where $0 < c < 1$ ?

Answer: Horizontal stretch by a factor of $\frac{1}{c}$ . Input coefficient less than 1 stretches horizontally.

Flashcard 57: Identify the transformation of $f(x) = x^2$ to $f(x) = 2x^2 + 3$ .

Answer: Vertical stretch by 2 and shift up by 3. Multiplies output by 2, then adds 3 to result.

Flashcard 58: What is the effect of $f(x)$ to $f(x) + c$ on its range?

Answer: Add $c$ to each element of the range. Vertical shift adds constant to all output values.

Flashcard 59: What is the effect of $f(x) + c$ on the graph of $f(x)$ ?

Answer: Vertical shift upward by $c$ units. Adding constant to function output moves graph up.

Flashcard 60: What is the effect of $f(x) - c$ on the graph of $f(x)$ ?

Answer: Vertical shift downward by $c$ units. Subtracting constant from function output moves graph down.

Flashcard 61: Identify the transformation: $f(x) = |x|$ to $f(x) = 2|x|$

Answer: Vertical stretch by a factor of 2. Coefficient 2 multiplies all $y$ -values by 2.

Flashcard 62: What is the combined effect of $-f(x + 2)$ ?

Answer: Reflection across x-axis and left shift by 2. Combines vertical reflection and horizontal translation.

Flashcard 63: Identify the transformation of $f(x) = x^2$ to $f(x) = 2x^2 + 3$ .

Answer: Vertical stretch by 2 and shift up by 3. Multiplies output by 2, then adds 3 to result.

Flashcard 64: What is the effect of $f(x)$ to $f(x + c)$ on its domain?

Answer: Subtract $c$ from each element of the domain. Horizontal shift adjusts input values by constant.

Flashcard 65: Identify the transformation: $f(x) = |x|$ to $f(x) = 3|x|$

Answer: Vertical stretch by a factor of 3. Factor 3 multiplies all $y$ -values by 3.

Flashcard 66: What transformation does $f(x) = x^2$ to $f(x) = (x - 6)^2$ represent?

Answer: Horizontal shift right by 6 units. Subtracting 6 from input shifts right by 6.

Flashcard 67: Identify the transformation: $f(x) = x^2$ to $f(x) = x^2 + 5$

Answer: Vertical shift upward by 5 units. Adding 5 to function output shifts graph upward.

Flashcard 68: What is the effect of $f(cx)$ where $c > 1$ ?

Answer: Horizontal compression by a factor of $\frac{1}{c}$ . Input coefficient greater than 1 compresses horizontally.

AP Precalculus Flashcards: Transformations Of Functions

Transformations Of Functions

What this deck covers

How to use these flashcards

All flashcards

Flashcard 1: Identify the transformation: f(x)=1xf(x) = \frac{1}{x}f(x)=x1​ to f(x)=1−xf(x) = \frac{1}{-x}f(x)=−x1​

Flashcard 2: What is the effect of cf(x)cf(x)cf(x) where 0<c<10 < c < 10<c<1?

Flashcard 3: Identify the transformation: f(x)=∣x∣f(x) = |x|f(x)=∣x∣ to f(x)=2∣x∣f(x) = 2|x|f(x)=2∣x∣

Flashcard 4: What is the effect of f(x)f(x)f(x) to f(x+c)f(x + c)f(x+c) on its domain?

Flashcard 5: Identify the transformation: f(x)=exf(x) = e^xf(x)=ex to f(x)=e−xf(x) = e^{-x}f(x)=e−x

Flashcard 6: What transformation does −f(x)-f(x)−f(x) represent?

Flashcard 7: What is the effect of cf(x)cf(x)cf(x) where c>1c > 1c>1?

Flashcard 8: Identify the transformation: f(x)=x3f(x) = x^3f(x)=x3 to f(x)=x3−2f(x) = x^3 - 2f(x)=x3−2

Flashcard 9: Identify the transformation: f(x)=1xf(x) = \frac{1}{x}f(x)=x1​ to f(x)=1x+1f(x) = \frac{1}{x} + 1f(x)=x1​+1

Flashcard 10: What transformation is applied: f(x)=1xf(x) = \frac{1}{x}f(x)=x1​ to f(x)=1(x−4)f(x) = \frac{1}{(x-4)}f(x)=(x−4)1​?

Flashcard 11: Identify the transformation: f(x)=1xf(x) = \frac{1}{x}f(x)=x1​ to f(x)=1x−5f(x) = \frac{1}{x} - 5f(x)=x1​−5

Flashcard 12: What is the effect of f(x−c)f(x - c)f(x−c) on the graph of f(x)f(x)f(x)?

Flashcard 13: What is the effect of f(x)f(x)f(x) to f(−x)f(-x)f(−x) on its domain?

Flashcard 14: Identify the transformation: f(x)=1xf(x) = \frac{1}{x}f(x)=x1​ to f(x)=1x+7f(x) = \frac{1}{x} + 7f(x)=x1​+7

Flashcard 15: What is the effect of cf(x)cf(x)cf(x) where 0<c<10 < c < 10<c<1?

Flashcard 16: What is the effect of f(x)−cf(x) - cf(x)−c on the graph of f(x)f(x)f(x)?

Flashcard 17: What is the combined effect of −f(x+2)-f(x + 2)−f(x+2)?

Flashcard 18: Identify the transformation: f(x)=∣x∣f(x) = |x|f(x)=∣x∣ to f(x)=∣x+2∣f(x) = |x + 2|f(x)=∣x+2∣

Flashcard 19: What is the effect of cf(x)cf(x)cf(x) where c>1c > 1c>1?

Flashcard 20: Identify the transformation: f(x)=1xf(x) = \frac{1}{x}f(x)=x1​ to f(x)=1x−3f(x) = \frac{1}{x} - 3f(x)=x1​−3

Flashcard 21: What transformation does f(−x)f(-x)f(−x) represent?

Flashcard 22: Identify the transformation: f(x)=x2f(x) = x^2f(x)=x2 to f(x)=x2+5f(x) = x^2 + 5f(x)=x2+5

Flashcard 23: Identify the transformation: f(x)=∣x∣f(x) = |x|f(x)=∣x∣ to f(x)=∣x−1∣f(x) = |x - 1|f(x)=∣x−1∣

Flashcard 24: What transformation does f(x)=x2f(x) = x^2f(x)=x2 to f(x)=−x2f(x) = -x^2f(x)=−x2 represent?

Flashcard 25: What transformation is applied: f(x)=1xf(x) = \frac{1}{x}f(x)=x1​ to f(x)=1(x−4)f(x) = \frac{1}{(x-4)}f(x)=(x−4)1​?

Flashcard 26: Identify the transformation: f(x)=1xf(x) = \frac{1}{x}f(x)=x1​ to f(x)=1x+1f(x) = \frac{1}{x} + 1f(x)=x1​+1

Flashcard 27: Identify the transformation: f(x)=∣x∣f(x) = |x|f(x)=∣x∣ to f(x)=3∣x∣f(x) = 3|x|f(x)=3∣x∣

Flashcard 28: What is the effect of f(x)f(x)f(x) to −f(x)-f(x)−f(x) on its range?

Flashcard 29: What transformation does f(x)=x2f(x) = x^2f(x)=x2 to f(x)=(x+5)2f(x) = (x + 5)^2f(x)=(x+5)2 represent?

Flashcard 30: Identify the transformation: f(x)=1xf(x) = \frac{1}{x}f(x)=x1​ to f(x)=1x−5f(x) = \frac{1}{x} - 5f(x)=x1​−5

Flashcard 31: Identify the transformation: f(x)=x2f(x) = x^2f(x)=x2 to f(x)=(x−3)2f(x) = (x - 3)^2f(x)=(x−3)2

Flashcard 32: Identify the transformation: f(x)=x3f(x) = x^3f(x)=x3 to f(x)=x3−2f(x) = x^3 - 2f(x)=x3−2

Flashcard 33: What is the effect of f(cx)f(cx)f(cx) where c>1c > 1c>1?

Flashcard 34: What is the effect of f(x)f(x)f(x) to −f(x)-f(x)−f(x) on its range?

Flashcard 35: What is the effect of f(x)f(x)f(x) to cf(x)cf(x)cf(x) where c<0c < 0c<0?

Flashcard 36: Identify the transformation: f(x)=1xf(x) = \frac{1}{x}f(x)=x1​ to f(x)=1x−3f(x) = \frac{1}{x} - 3f(x)=x1​−3

Flashcard 37: Identify the transformation: f(x)=x3f(x) = x^3f(x)=x3 to f(x)=(x+4)3f(x) = (x + 4)^3f(x)=(x+4)3

Flashcard 38: Identify the transformation: f(x)=1xf(x) = \frac{1}{x}f(x)=x1​ to f(x)=1x+2f(x) = \frac{1}{x+2}f(x)=x+21​

Flashcard 39: What is the effect of f(cx)f(cx)f(cx) where 0<c<10 < c < 10<c<1?

Flashcard 40: What is the effect of f(x+c)f(x + c)f(x+c) on the graph of f(x)f(x)f(x)?

Flashcard 41: Identify the transformation: f(x)=x3f(x) = x^3f(x)=x3 to f(x)=(x+4)3f(x) = (x + 4)^3f(x)=(x+4)3

Flashcard 42: What is the effect of f(x+c)f(x + c)f(x+c) on the graph of f(x)f(x)f(x)?

Flashcard 43: What is the effect of f(x)f(x)f(x) to cf(x)cf(x)cf(x) where c<0c < 0c<0?

Flashcard 44: What is the effect of f(x)f(x)f(x) to f(x)+cf(x) + cf(x)+c on its range?

Flashcard 45: What transformation does f(x)=x2f(x) = x^2f(x)=x2 to f(x)=(x−6)2f(x) = (x - 6)^2f(x)=(x−6)2 represent?

Flashcard 46: What is the effect of f(x)f(x)f(x) to f(−x)f(-x)f(−x) on its domain?

Flashcard 47: Identify the transformation: f(x)=1xf(x) = \frac{1}{x}f(x)=x1​ to f(x)=1−xf(x) = \frac{1}{-x}f(x)=−x1​

Flashcard 48: What is the effect of f(x−c)f(x - c)f(x−c) on the graph of f(x)f(x)f(x)?

Flashcard 49: Identify the transformation: f(x)=x2f(x) = x^2f(x)=x2 to f(x)=(x−3)2f(x) = (x - 3)^2f(x)=(x−3)2

Flashcard 50: Identify the transformation: f(x)=1xf(x) = \frac{1}{x}f(x)=x1​ to f(x)=1x+7f(x) = \frac{1}{x} + 7f(x)=x1​+7

Flashcard 51: Identify the transformation: f(x)=∣x∣f(x) = |x|f(x)=∣x∣ to f(x)=∣x−1∣f(x) = |x - 1|f(x)=∣x−1∣

Flashcard 52: What transformation does f(−x)f(-x)f(−x) represent?

Flashcard 53: Identify the transformation: f(x)=∣x∣f(x) = |x|f(x)=∣x∣ to f(x)=∣x+2∣f(x) = |x + 2|f(x)=∣x+2∣

Flashcard 54: What transformation does f(x)=x2f(x) = x^2f(x)=x2 to f(x)=−x2f(x) = -x^2f(x)=−x2 represent?

Flashcard 55: What is the effect of f(x)+cf(x) + cf(x)+c on the graph of f(x)f(x)f(x)?

Flashcard 56: What is the effect of f(cx)f(cx)f(cx) where 0<c<10 < c < 10<c<1?

Flashcard 57: Identify the transformation of f(x)=x2f(x) = x^2f(x)=x2 to f(x)=2x2+3f(x) = 2x^2 + 3f(x)=2x2+3.

Flashcard 58: What is the effect of f(x)f(x)f(x) to f(x)+cf(x) + cf(x)+c on its range?

Flashcard 59: What is the effect of f(x)+cf(x) + cf(x)+c on the graph of f(x)f(x)f(x)?

Flashcard 60: What is the effect of f(x)−cf(x) - cf(x)−c on the graph of f(x)f(x)f(x)?

Flashcard 61: Identify the transformation: f(x)=∣x∣f(x) = |x|f(x)=∣x∣ to f(x)=2∣x∣f(x) = 2|x|f(x)=2∣x∣

Flashcard 62: What is the combined effect of −f(x+2)-f(x + 2)−f(x+2)?

Flashcard 63: Identify the transformation of f(x)=x2f(x) = x^2f(x)=x2 to f(x)=2x2+3f(x) = 2x^2 + 3f(x)=2x2+3.

Flashcard 64: What is the effect of f(x)f(x)f(x) to f(x+c)f(x + c)f(x+c) on its domain?

Flashcard 65: Identify the transformation: f(x)=∣x∣f(x) = |x|f(x)=∣x∣ to f(x)=3∣x∣f(x) = 3|x|f(x)=3∣x∣

Flashcard 66: What transformation does f(x)=x2f(x) = x^2f(x)=x2 to f(x)=(x−6)2f(x) = (x - 6)^2f(x)=(x−6)2 represent?

Flashcard 67: Identify the transformation: f(x)=x2f(x) = x^2f(x)=x2 to f(x)=x2+5f(x) = x^2 + 5f(x)=x2+5

Flashcard 68: What is the effect of f(cx)f(cx)f(cx) where c>1c > 1c>1?