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Algebra 1 : Algebra 1

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Example Questions

Example Question #3351 : Algebra 1

Each of the following 4 sets defines a relationship between and . Which of these four sets defines a one-to-one function:

A = $\left \{ \left ( 1,2 \right )\left ( 2,3 \right )\left ( 3,4 \right )\left ( 4,5 \right ) \right \}$

B= $\left \{ \left ( 1,3 \right )\left ( 2,3 \right )\left ( 3,5 \right )\left ( 4,5 \right ) \right \}$

C = $\left \{ \left ( 1,2 \right )\left ( 2,3 \right )\left ( 2,4 \right )\left ( 2,5 \right )\left ( 6,7\right )\left\right \}$

D = $\left \{ \left ( 1,7 \right )\left ( 2,7 \right )\left ( 3,7 \right )\left ( 4,7 \right ) \right \}$

Possible Answers:

Set C

Set D

Set A and Set B

Set A

Set B

Correct answer:

Set A

Explanation:

Only in set A one can see that there is an unique value of for each value of and similarly each of the values maps into one and only one value. Hence set A must define a one-to-one function.

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Example Question #3352 : Algebra 1

Which of the following equations does not represent a function?

A) y = 3

B) y = 3x +5

$C) y = -x^{2} + 3$

$D) y^{2} = x^{2}-5$

$E) y = 2^{x}$

Possible Answers:

Correct answer:

Explanation:

The correct answer is equation D. If we solve for we get

$y = \pm \sqrt{x^{2}-5}$

The fact that each value of gives us two values of $\left ( \pm )$ disqualifies it as a function.

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Example Question #241 : Grade 8

Which of the following equations represents a one-to-one function:

A) y = 3

B) y = 3x +5

$C) y = 3x^{2}-5$

$D) y^{2}= x^{2} - 5$

E) x = -3

Possible Answers:

Correct answer:

Explanation:

Only equation B maps each value of into a unique value of and in a similar way each and every value of maps into one and only one value of .

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Example Question #3353 : Algebra 1

Test whether the given function is symmetric with respect to the -axis, -axis, origin.

$y = x^{3}-x^{2}$

Possible Answers:

y axis

x axis

All of the above

origin

Not symmetric with respect to x axis, y axis, and the origin

Correct answer:

Not symmetric with respect to x axis, y axis, and the origin

Explanation:

Since $y = \left ( -x \right )^{3} -\left ( -x \right )^{2} = -x^{3}-x^{2} \neq y$

It is not symmetric with respect the -axis

$-f\left ( x \right ) = -y = -\left ( x^{3}-x^{2} \right ) = -x^{3}+x^{2}\neq f\left ( x \right )$

It is not symmetric with respect to the -axis

$-y = \left ( -x)^{3}-\left ( -x \right )^{2} = -x^{3}-x^{2}=-\left ( x^{3} \right +x^{2})$

Hence multiplying by both sides we get

$y = x^{3}+x^{2}$

Hence it is not symmetric with respect to the origin.

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Example Question #21 : How To Find F(X)

A function is defined by the following set of ordered pairs:

$\left \{ (1,5), (2,4), (3,2), (4,3), (5,5) \right \}$

What is its inverse?

Possible Answers:

$\left \{ (1,-5), (2,-4), (3,-2), (4,-3), (5,-5) \right \}$

The function does not have an inverse.

$\left \{ (5,1), (4,2), (2,3), (3,4), (5,5) \right \}$

$\left \{ (5,1), (4,2), (2,3), (3,4)\right \}$

$\left \{ (-1,5), (-2,4), (-3,2), (-4,3), (-5,5) \right \}$

Correct answer:

The function does not have an inverse.

Explanation:

The inverse of a function is the relation that switches the positions of the coordinates of each ordered pair. However, for a function to have an inverse, the result of those switches must itself be a function. The switches yield the relation

$\left \{ (5,1), (4,2), (2,3), (3,4), (5,5) \right \}$

which is not a function, since the -coordinate 5 is paired with two -coordinates, 1 and 5.

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Example Question #71 : Functions And Lines

What is the inverse of the function defined by the following set of ordered pairs?

$\left \{ (1,9), (2,8), (3,7), (4,6), (5,5) \right \}$

Possible Answers:

$\left \{ (-1,-9), (-2,-8), (-3,-7), (-4,-6), (-5,-5) \right \}$

$\left \{ (1,-9), (2,-8), (3,-7), (4,-6), (5,-5) \right \}$

$\left \{ \left(1,\frac{1}{9} \right ), \left(2,\frac{1}{8} \right ), \left(3,\frac{1}{7} \right ), \left(4,\frac{1}{6} \right ), \left(5,\frac{1}{5} \right ) \right \}$

$\left \{ (9,1), (8,2), (7,3), (6,4), (5,5) \right \}$

The function does not have an inverse.

Correct answer:

$\left \{ (9,1), (8,2), (7,3), (6,4), (5,5) \right \}$

Explanation:

The inverse of a function is the relation that switches the positions of the coordinates of each ordered pair. Therefore, the correct choice is

$\left \{ (9,1), (8,2), (7,3), (6,4), (5,5) \right \}$ .

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Example Question #72 : Functions And Lines

Find the inverse of this function.

$y=\frac{x}{x-3}$

Possible Answers:

No inverse exists

$y=\frac{3x}{1-x}$

$y=\frac{-3x}{1-x}$

$y=\frac{-3x^{2}}{1-x^{2}}$

$y=\frac{-3x}{1+x}$

Correct answer:

$y=\frac{-3x}{1-x}$

Explanation:

The inverse of an equation is given by solving for the x value in terms of y. To find the inverse, take the original equation, $y=\frac{x}{x-3}$ , and solve for x.

First multiply both sides by (x – 3).

y(x-3)=x

Distribute y into the parenthesis.

xy-3y=x

Subtract xy to both sides.

-3y=x-xy

Factor the x.

-3y=x(1-y)

Divide both sides by (1 – y).

$x=\frac{-3y}{1-y}$

Once you have solved for x, switch the x and y terms.

$y=\frac{-3x}{1-x}$

Though an inverse function is found by solving for x, it still must follow the "y=" convention.

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Example Question #22 : How To Find F(X)

Given $f{\left (x \right )}= x^{2} - 5, g\left ( x \right ) = 2x -3$

Find $f\cdot g\left ( x \right )\ OR\ f( g\left ( x \right ))$ .

Possible Answers:

$4x^{2}+4$

$4x^{2}-6x +5$

2x-8

$x^{2}+2x -8$

$4x^{2}-12x + 4$

Correct answer:

$4x^{2}-12x + 4$

Explanation:

$f\left ( x \right ) = x^{2} -5$

Replacing or substituting g(x) for in $f\left ( x \right )$ we get $f(g\left ( x \right ))=$

$\left ( 2x-3 \right )^{2}-5$

When simplified we get

$4x^{2}-12x +4$

which is the correct answer.

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Example Question #23 : How To Find F(X)

Given $f\left ( x \right ) = x^{2}-5\ and\ g(x) = 2x-3$

Find $g\bullet f\left ( x \right ) = g\left ( f\left ( x \right ) \right )$ .

Possible Answers:

$2x^{2} - 13$

$x^{2}+2x -8$

$\left ( 2x-3 \right )^{2}$

$4x^{2}-12x+4$

$2x^{2}-10$

Correct answer:

$2x^{2} - 13$

Explanation:

$g\left ( f\left ( x \right ) \right ) = 2\left ( x^{2} \right - 5) -3$

which is equal to

$2x^{2} - 13$

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Example Question #22 : How To Find F(X)

Given $f\left ( x \right ) = x^{2} - 5$ .

Find $f\left ( f\left ( x \right ) \right )$ .

Possible Answers:

$\left (x^{2} - 5\right )^{2}$

$x^{4} - 10x^{2} + 20$

$\left ( x^{2}\ - 5)^{4}$

$x^{2} - 10$

$x^{2} - 5$

Correct answer:

$x^{4} - 10x^{2} + 20$

Explanation:

Given $f\left ( x \right )$ = $x^{2}- 5$

Replacing in the above equation with $f\left ( x \right )$

one gets $\left ( x^{2} - 5\right )^{2} -5$

Upon simplification one gets the correct answer which is

$x^{4}-10x^{2} + 20$

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Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #3351 : Algebra 1

Example Question #3352 : Algebra 1

Example Question #241 : Grade 8

Example Question #3353 : Algebra 1

Example Question #21 : How To Find F(X)

Example Question #71 : Functions And Lines

Example Question #72 : Functions And Lines

Example Question #22 : How To Find F(X)

Example Question #23 : How To Find F(X)

Example Question #22 : How To Find F(X)

All Algebra 1 Resources

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