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Algebra II : Functions and Graphs

Study concepts, example questions & explanations for Algebra II

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Example Questions

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

Solve the function for . When f(x)=16

What does equal when, f(x)=16

$f(x)=x^{2}-9$

Possible Answers:

$\pm5$

$\sqrt{5}$

-5

Correct answer:

$\pm5$

Explanation:

Plug 16 in for f(x) . 16=x^2-9

Add 9 to both sides. x^2=25

Take the square root of both sides. $\sqrt{25}$ = $\sqrt{x^{2}}$

Final answer is $\pm5$

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Example Question #371 : Algebra Ii

Evaluate $\small f(g(3))$ if f(x)=6x-4 and g(x)=x^2 .

Possible Answers:

196

Undefined

Correct answer:

Explanation:

$\small f(g(3))$

This expression is the same as saying "take the answer of $\small g(3)$ and plug it into $\small f(x)$ ."

First, we need to find $\small g(3)$ . We do this by plugging $\small 3$ in for $\small x$ in $\small g(x)$ .

g(x)=x^2

g(3)=3^2=9

Now we take this answer and plug it into $\small f(x)$ .

f(g(3))=f(9)

We can find the value of $\small f(9)$ by replacing $\small x$ with $\small 9$ .

f(x)=6x-4

f(9)=6(9)-4=50

This is our final answer.

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Example Question #2 : Function Notation

Orange Taxi company charges passengers a $4.50 base fase, plus $0.10 per mile driven. Write a function to represent the cost of a cab ride, in terms of number of miles driven, .

Possible Answers:

f(x) = 4.5^x

f(x) = x + 4.5^x

f(x) = 0.1 + 4.5x

f(x) = 4.5 + 1^x

$\displaystyle f(x) = 4.5 + 0.1x$

Correct answer:

$\displaystyle f(x) = 4.5 + 0.1x$

Explanation:

Total cost of the cab ride is going to equal the base fare ($4.50) plus an additional 10 cents per mile. This means the ride will always start off at $4.50. As the cab drives, the cost will increase by $0.10 each mile. This is represented as $0.10 times the number of miles. Therefore the total cost is:

f(x) = 4.5 + 0.1x

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Example Question #2 : Function Notation

A small office building is to be built with long walls feet long and short walls feet long each. The total length of the walls is to be 150 feet.

Write an equation for in terms of .

Possible Answers:

y = 150 - 4x

y = 75 - 2x

y = 2x - 75

y = 2x + 150

Correct answer:

y = 75 - 2x

Explanation:

The pre-question text provides us with all of the information required to complete this problem.

We know that the total length of the walls is to be 150 ft.

We also know that we have a total of 2 y walls and walls.

With this, we can set up an equation and solve for .

Our equation will be with sum of all the walls set equal to the total length of the wall...

2y + 4x = 150

Remeber, we want in terms of , which means our equation should look like

something

2y + 4x = 150 Subtract on both sides

2y = 150 - 4x Divide by on both sides

2y/2 = (150-4x)/2 Simplify

Answer!!!

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Example Question #2 : Function Notation

What is the slope of the function f(x)= -5x+3 ?

Possible Answers:

$\frac{3}{5}$

$-\frac{5}{3}$

Correct answer:

Explanation:

The function is written in slope-intercept form, which means:

y = mx+b

where:

= slope

= x value

= y-intercept

Therefore, the slope is ${\color{Red} -5}$

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Example Question #653 : Algebra Ii

A cable company charges a flat $29.99 activation fee, and an additional $12.99 per month for service. How would a function of the cost be represented in terms of months of service, ?

Possible Answers:

f(x)=12.99 +29.99x

This cannot be written as a function

f(x)=17x

f(x)=41.98x

f(x)=29.99+12.99x

Correct answer:

f(x)=29.99+12.99x

Explanation:

f(x)= 29.99+12.99x

The flat rate of 29.99 does not change depending on months of service. It is $29.99 no matter how long services are in use. The monthy fee is directly related to the number of months the services are in use.

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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 #3 : 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 #11 : Function Notation

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

Possible Answers:

f(a+h) -f(a)

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

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

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

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

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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Algebra II : Functions and Graphs

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

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

Example Question #371 : Algebra Ii

Example Question #2 : Function Notation

Example Question #2 : Function Notation

Example Question #2 : Function Notation

Example Question #653 : Algebra Ii

Example Question #5 : Function Notation

Example Question #7 : Function Notation

Example Question #3 : Function Notation

Example Question #11 : Function Notation

All Algebra II Resources

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