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Algebra 1 : Algebraic Functions

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Example Questions

Example Question #41 : Algebraic Functions

$\textup{If }f(p)= p^{3}-3p,\;\textup{what is the value of }f(5)\textup{?}$

Possible Answers:

107

110

140

Correct answer:

110

Explanation:

$\textup{Just plug in 5 every time you see }p\textup{ in the equation and solve:}$

$\left ( 5\right )^{3}-3\left ( 5\right )=125-15=110$

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Example Question #14 : Function Notation

$\textup{If }f\left(x\right )=\frac{3x^{2}-2x}{x}\textup{ , what is the value of}f\left ( 4\right )\textup{?}$

Possible Answers:

Correct answer:

Explanation:

$\textup{Plug in 4 every time you see an }x\textup{ in the given equation and solve:}$

$f\left ( 4\right )=\frac{3\left ( 4\right )^{2}-2\left ( 4\right )}{4}\;\;=\frac{48-8}{4}=10$

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Example Question #91 : Functions And Lines

$\small f(x)=2x+17$ .

Find $\small f(-3)$ .

Possible Answers:

$\small 23$

$\small 11$

$\small 16$

$\small 34$

Correct answer:

$\small 11$

Explanation:

Finding $\small f(-3)$ means plugging in $\small -3$ in place of x into the function $\small f(x)$ . In this case, we are told that $\small f(x)=2x+17$ , so we are multiplying $\small -3$ by 2 and then adding 17:

$\small \small f(-3)=2(-3)+17$ order of opperations tells us to first multiply:

$\small f(-3)=-6+17$ and now add:

$\small f(-3)= 11$

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Example Question #43 : How To Find F(X)

$\small f(x)=(2x)^2$ .

Evaluate $\small f(5)$ .

Possible Answers:

$\small 50$

$\small 100$

$\small 25$

Correct answer:

$\small 100$

Explanation:

Evaluating f(5) means plugging 5 in for x in the function $\small f(x)$ . In this case, we are told that $\small f(x)=(2x)^2$ , so that is what we will do to 5 - multiply by 2, then square the product:

$\small f(5)=(2*5)^2$ order of opperations [PEMDAS] tells us that first we will be doing what is in the parentheses, so we will multiply first:

$\small f(5)=10^2$ now we can square 10 for the final answer:

$\small f(5)=100$

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Example Question #43 : Algebraic Functions

$\small k(x)=3x^2 - 10$ .

Find $\small k(2)$ .

Possible Answers:

$\small 26$

$\small -1$

$\small 2$

Correct answer:

$\small 2$

Explanation:

Evaluating $\small k(2)$ means plugging in 2 for x in the function $\small k(x)$ . In this case we are told that $\small k(x)=3x^2 - 10$ , so that is what we'll do with 2:

$\small \small \small k(2)=3*2^2 - 10$ Order of opperations [PEMDAS] tells us to do parentheses first, but no opperations are taking place in parentheses. Next we will do exponents:

$\small k(2)=3*4 -10$ The next step in order of opperations is multiplication, so we will next multiply 3 and 4:

$\small k(2)=12-10$ finally we will subtract:

$\small k(2)=2$

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Example Question #42 : How To Find F(X)

If f(x) is the reciprocal of the following function what is f(x) ?

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

Possible Answers:

$\frac{x}{(y-x)^3}$

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

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

$\frac{-x^3}{y+x}$

x^3(y-x)

Correct answer:

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

Explanation:

The question is asking for the reciprocal.

The reciprocal can be found by flipping the numerator and the denominator, effectively dividing 1 by the number.

$\frac{x^3}{y-x}$ becomes $\frac{y-x}{x^3}$ .

*Always remember what the question is asking.

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Example Question #1 : Understand Functions: Ccss.Math.Content.8.F.A.1

$f(x) = \frac{x^{4}-x+\sqrt[3]{x}}{x^{x}+3x}$

Find f(1) .

Possible Answers:

$\frac{1}{3}$

Undefined

$\frac{1}{4}$

Correct answer:

$\frac{1}{4}$

Explanation:

This question demonstrates that complicated functions are not complicated at every point.

To solve the function at x=1, all that is necessary is familiarity with the operations used.

$f(1) = \frac{1^{4}-1+\sqrt[3]{1}}{1^{1}+3(1)}$

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

$=\frac{1}{4}$

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Example Question #43 : How To Find F(X)

Given a function $f(x)=3x^{2}+8x+2$ , what is f(4) ?

Possible Answers:

Correct answer:

Explanation:

Given a function $f(x)=3x^{2}+8x+2$ , we can plug in x=4 to get

$\\f(4)=3(4)^{2}+8(4)+2\\f(4)=3(16)+32+2\\f(4)=48+32+2\\f(4)=48+34\\f(4)=82$

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Example Question #44 : How To Find F(X)

Given a function $f(x)=5x-x^{2}+7$ , what is f(-2) ?

Possible Answers:

Correct answer:

Explanation:

Given a function $f(x)=5x-x^{2}+7$ , we can plug in x=-2 to get

$\\f(-2)=5(-2)-(-2)^{2}+7\\=-10-4+7\\=-14+7\\=-7$ .

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Example Question #45 : How To Find F(X)

Given a function $f(x)=\frac{1}{2}x^{2}+7x-3$ , what is f(5) ?

Possible Answers:

$-\frac{2}{89}$

$\frac{2}{89}$

None of the above

$-\frac{89}{2}$

$\frac{89}{2}$

Correct answer:

$\frac{89}{2}$

Explanation:

Given a function $f(x)=\frac{1}{2}x^{2}+7x-3$ , we can plug in x=5 to get

$\\f(5)=\frac{1}{2}(5)^{2}+7(5)-3\\ \\=\frac{25}{2}+35-3\\ \\=\frac{25}{2}+32\\ \\=\frac{25}{2}+\frac{64}{2}\\ \\=\frac{89}{2}$

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Algebra 1 : Algebraic Functions

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #41 : Algebraic Functions

Example Question #14 : Function Notation

Example Question #91 : Functions And Lines

Example Question #43 : How To Find F(X)

Example Question #43 : Algebraic Functions

Example Question #42 : How To Find F(X)

Example Question #1 : Understand Functions: Ccss.Math.Content.8.F.A.1

Example Question #43 : How To Find F(X)

Example Question #44 : How To Find F(X)

Example Question #45 : How To Find F(X)

All Algebra 1 Resources

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