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Algebra II : Function Notation

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Example Question #2 : How To Use The Quadratic Function

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

Possible Answers:

f(a+h) -f(a)

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

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

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

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

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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Example Question #32 : Algebraic Functions

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

Possible Answers:

f(3)=3

f(3)=5

f(3)=16

Does not exist

f(3)=9

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 #11 : Function Notation

What is f(7) of the following equation?

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

Possible Answers:

189

188

187

190

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 #141 : Functions And Graphs

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

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 #141 : Functions And Graphs

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

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 #13 : Function Notation

f(x)=x+6

If f(x)=10 , find .

Possible Answers:

$\small 10$

$\small 4$

$\small -10$

$\small -4$

$\small 16$

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 #14 : 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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Example Question #11 : Function Notation

Given f(x) and g(x) , find f(g(5)) .

f(x)=x^4-x+15

g(x)=x^2+3x-25

Possible Answers:

50625

Undefined

225

Correct answer:

50625

Explanation:

Given f(x) and g(x), find f(g(5))

f(x)=x^4-x+15

g(x)=x^2+3x-25

This type of problem can look intimidating depending on how it is set up. What it is asking is for us to plug g(x) into f(x) everywhere we see an x, and then to plug in 5 everywhere we still have an x. It gets a little cumbersome if approached all at once:

f(g(x))=(x^2+3x-25)^4-(x^2+3x-25)+15

This looks a bit unwieldy, but this problem can be approached easily by looking at it in layers.

First, find g(5)

g(5)=(5)^2+3(5)-25=25-25+15=15

g(5)=15 .

Next, plug that 15 into f(x).

f(g(5))=f(15)=(15)^4-15+15=15^4=50625

So our answer is:

50625

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Example Question #16 : Function Notation

If f(x)= x^2 + 4 and g(x)= x-3 , what is f(g(x)) ?

Possible Answers:

x^2 - 2x + 3

x+1

x^2 - 6x + 13

x^2 + 1

Correct answer:

x^2 - 6x + 13

Explanation:

We start by replacing all the 's in f(x) with the entire function of g(x) :

f(g(x))= (x-3)^2 + 4

We then FOIL the first term:

f(g(x))= (x^2 - 6x + 9) +4

And we collect all the like terms (the constants in this case):

f(g(x))= x^2 - 6x + 13

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Example Question #17 : Function Notation

What is

$(f\cdot g)(x)$ ?

f(x) = -8x+8

g(x) = x^2

Possible Answers:

2x^3-4

8x^2-8

-8x^3+8x^2

8x^3 -12

4x^2-4x

Correct answer:

-8x^3+8x^2

Explanation:

To find the composition of two functions, substitute the second equation in to the first function.

$(g\cdot h)(x)=g(h(x))$

Therefore,

$(f\cdot g)(x) = (-8x+8)(x^2)$

-8x(x^2) =-8x^3

and

8(x^2) = 8x^2

Thus,

$(f\cdot g)(x)= -8x^3+8x^2$ .

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Algebra II : Function Notation

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #2 : How To Use The Quadratic Function

Example Question #32 : Algebraic Functions

Example Question #11 : Function Notation

Example Question #141 : Functions And Graphs

Example Question #141 : Functions And Graphs

Example Question #13 : Function Notation

Example Question #14 : Function Notation

Example Question #11 : Function Notation

Example Question #16 : Function Notation

Example Question #17 : Function Notation

All Algebra II Resources

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