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Algebra II : Algebra II

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Example Questions

Example Question #5 : Function Notation

Find f(3) for the following function:

$f(x)=\frac{4x+3}{x^2}$

Possible Answers:

$\frac{5}{3}$

$\frac{12x+9}{x^2}$

Correct answer:

$\frac{5}{3}$

Explanation:

To evaluate f(3) , we just plug in a wherever we see an in the function, so our equation becomes

$f(3)=\frac{3\cdot 4+3}{3^2}$

which is equal to

$f(3)=\frac{5}{3}$

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Example Question #7 : Function Notation

Find f(g+h) for the following function:

f(x)=cos(5x^2)e^x

Possible Answers:

$cos(5g^2)e^{g}+cos(5h^2)e^{h}$

$cos(5g^2e^{g})+cos(5h^2e^{h})$

$cos(5g^2+5h^2)e^{g+h}$

$cos(5g^2+10gh+5h^2)e^{g+h}$

$cos(5g^2+10gh+5h^2)e^{g}+e^h$

Correct answer:

$cos(5g^2+10gh+5h^2)e^{g+h}$

Explanation:

To find f(g+h) , all we do is plug in (g+h) wherever we see an in the function. We have to be sure we keep the parentheses. In this case, when we plug in (g+h) , we get

$cos(5(g+h)^2)e^{g+h}$

Then, when we expand our binomial squared and distribute the , we get

$cos(5g^2+10gh+5h^2)e^{g+h}$

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Example Question #2 : Function Notation

If f(x)=g(x)-3 , and $g(x)=x^{2} -1$ , for which of the following value(s) will f(x) be an odd number?

Possible Answers:

Correct answer:

Explanation:

First, x needs to be plugged into g(x).

Then, the resulting solution needs to be substituted into f(x).

For example,

g(7) = 49-1 = 48 .

f(7) = g(7)-3 = 48-3 = 45

Since 45 is an odd number, 7 is an x value that gives this result. Because both equations subtract an odd number to get the final result, only an odd number will result in an odd result therefore, none of the other options will give an odd result.

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Example Question #131 : Introduction To Functions

Given $f(x) = -2x^{2} - 3x +5$ , find f(a+h) - f(a) .

Possible Answers:

$-2h^{2} - 4ah -3h$

f(a+h) -f(a)

$-2a^{2}-4ah-2h^{2} -3a -3h +5$

$4ah+2h^{2} -3h$

$2a^{2}+3a-5$

Correct answer:

$-2h^{2} - 4ah -3h$

Explanation:

Plug in a for x:

$f(a)=-(-2a^{2}-3a+5) = 2a^2+3a-5$

Next plug in (a + h) for x:

$f(a+h) = -2(a+h)^2-3(a+h)+5 = -2a^{2} - 4ah - 2h^{2} -3a - 3h +5$

Therefore f(a+h) - f(a) = $-2h^{2} - 4ah - 3h$ .

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Example Question #11 : Function Notation

Solve for f(3) when $f(x)= \frac{x^{2}+12x}{3x}$ .

Possible Answers:

Does not exist

f(3)=3

f(3)=5

f(3)=9

f(3)=16

Correct answer:

f(3)=5

Explanation:

Plug 3 in for x:

$f(3)=\frac{(3^{2})+12*3}{3*3}$

Simplify:

= $\frac{9+36}{9}$

= 5

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Example Question #12 : Function Notation

What is f(7) of the following equation?

$f(x)=x^{2}+15x+35$

Possible Answers:

188

190

187

189

Correct answer:

189

Explanation:

To complete an equation with a function, plug the number inside the parentheses into the equation for and solve algebraically.

In this case the $f(7)=7^{2}+(15*7)+35$

Square the 7 and multiply to get f(7)=49+105+35

Add the numbers to get the answer f(7)=189 .

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Example Question #12 : Function Notation

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

Possible Answers:

110

140

107

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 #13 : 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 #15 : Function Notation

f(x)=x+6

If f(x)=10 , find .

Possible Answers:

$\small -10$

$\small 16$

$\small 10$

$\small 4$

$\small -4$

Correct answer:

$\small 4$

Explanation:

If f(x)=10 then f(x) can be rewritten as f(x)=10=x+6 . Therefore, 10=x+6 . Subtracting from both sides of the eqauation gives x=4 .

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Example Question #11 : Function Notation

Evaluate the function for f(-10) .

f(x)=x^2+8x-x+2

Possible Answers:

$\small 0$

Correct answer:

Explanation:

To solve for the value of the function at f(x)=-10 , simply plug in the value in place of every . By doing this, you will be left with the equation: f(-10)=(-10)^2+8(10)-(10)+2=32 .

Another way to go about the problem is first simplifying the expression so that like terms are collected, so f(x)=x^2+7x+2 . Then to find f(x)=-10 , simply plug in the value in place of every . By doing this, you will be left with the equation: f(-10)=(-10)^2+7(10)+2=32 .

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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #5 : Function Notation

Example Question #7 : Function Notation

Example Question #2 : Function Notation

Example Question #131 : Introduction To Functions

Example Question #11 : Function Notation

Example Question #12 : Function Notation

Example Question #12 : Function Notation

Example Question #13 : Function Notation

Example Question #15 : Function Notation

Example Question #11 : Function Notation

All Algebra II Resources

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