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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 : Function Notation

Given g(x) =x^2+2 and h(x)=3x , what is g(h(2)) ?

Possible Answers:

$\textup{The answer is not given.}$

Correct answer:

Explanation:

The question asked is a composite function.

Evaluate h(2) first. Replace x with the value of 2 in the function h(x) .

h(2)=3(2)=6

After substitution, evaluate g(6) . Replace x with the value of 6 in the function g(x) .

g(6) =(6)^2+2 = 36+2 =38

The answer is:

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Example Question #21 : Function Notation

If f(x) = 2x+3 , what must f(-6) be?

Possible Answers:

Correct answer:

Explanation:

Replace the value of negative six into the function of x equation.

f(-6) = 2(-6)+3

Simplify this equation.

-12+3 =-9

The answer is:

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Example Question #23 : Function Notation

If f(x)=1 and $g(x)= 2x^{5}+3x^{4}+4x^{3}$ , what must f(g(50)) be?

Possible Answers:

$\textup{Cannot be solved.}$

644250000

$\frac{1}{644250000}$

Correct answer:

Explanation:

Notice that this composite function is asking for the value of of a particular number solved by evaluating g(50) . The function f(x)=1 means that no matter what the x-value inside f(x) is, the final output will always be one.

We do not even need to evaluate g(50) to determine what f(g(50)) is since we know that g(50) will yield a very large number, and that the output of the function of f(x) will be one for $x=\textup{any constant}$ .

The answer is:

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Example Question #151 : Introduction To Functions

If f(x) = 3x-6 and g(x)= 9x-3 , what is $g(f(x))\cdot f(x)$ ?

Possible Answers:

81x^2-333x+342

81x^2-342

$\textup{The answer is not given.}$

81x^2+342

81x^2+333x-342

Correct answer:

81x^2-333x+342

Explanation:

Evaluate g(f(x)) first. Substitute the function f(x) into g(x) .

g( 3x-6)= 9( 3x-6)-3

Distribute the integer through the binomial and simplify the equation.

9( 3x-6)-3 = 27x-54-3 = 27x-57

g(f(x))=g( 3x-6)= 27x-57

Multiply this expression with f(x) .

(27x-57)(3x-6)

= (27x)(3x)+(27x)(-6)+(-57)(3x)+(-57)(-6)

81x^2-162x-171x+342

The answer is: 81x^2-333x+342

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Example Question #21 : Function Notation

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

Possible Answers:

6x+9x^3

6x+9x^2

6x+ 27x^2

9x^2

6x+ 27x^3

Correct answer:

6x+ 27x^2

Explanation:

Evaluate each term separately.

2f(x)=2(3x)=6x

The term g(f(x)) means to input the function f(x) into the function g(x) .

Substitute the equation as the replacement of the x-variable.

g(f(x)) = 3(3x)^2 = 3(9x^2) = 27x^2

Add the two terms.

2f(x)+g(f(x))=6x+ 27x^2

The answer is: 6x+ 27x^2

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Example Question #22 : Function Notation

Given the function: f(x) = x^3-2(x+2) , what is f(-4) ?

Possible Answers:

Correct answer:

Explanation:

To solve this function, the term f(-4) means to replace negative four with the x-variable.

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

Use order of operations and simplify the terms on the right side.

f(-4) = -64 -2(-2)

f(-4) = -64+4 = -60

The answer is:

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Example Question #27 : Function Notation

Given f(x) = 3x+3 and g(x)=-3 , what is g(f(x))+2g(x) ?

Possible Answers:

$\textup{The answer cannot be determined.}$

Correct answer:

Explanation:

Evaluate g(f(x)) first. If we plugged in the function f(x) = 3x+3 into the function g(x)=-3 , no matter what is replaced with, the final output will always be negative three.

g(3x+3)= -3

Evaluate 2g(x) . Multiply the function g(x)=-3 by two.

2g(x) = -6

Sum both numbers.

-3+(-6) = -3-6=-9

The answer is:

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Example Question #28 : Function Notation

If g(x)=1 , f(x)=2 , and $h(x)= \pi$ , what is 2f(g(x))+h(g(x)) ?

Possible Answers:

$\pi+1$

$\pi+2$

$2\pi+4$

$\pi +4$

$2\pi+2$

Correct answer:

$\pi +4$

Explanation:

Evaluate each term separately.

The term f(g(x)) means to input the function g(x)=1 into the function f(x) .

$2f(g(x)) = 2\cdot f(1) = 2\cdot 2 = 4$

Follow suit for h(g(x)) . Substitute g(x)=1 into the function h(x) .

$h(g(x)) =h(1)=\pi$

Add the two known terms.

$2f(g(x))+h(g(x)) = 4+\pi$

The answer is: $\pi +4$

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Example Question #29 : Function Notation

If g(x)=3x+5 , what is g(x+3) ?

Possible Answers:

3x+8

3x+11

3x+14

3x+55

3x+5

Correct answer:

3x+14

Explanation:

In order to solve g(x+3) , replace the entire quantity of (x+3) as a replacement of .

Replace the term.

g(x+3)=3(x+3)+5

Distribute the binomial.

3x+9+5 = 3x+14

The answer is: 3x+14

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Example Question #151 : Functions And Graphs

If h(x) = 2x^3 , what is h(h(2x^3)) ?

Possible Answers:

$\textup{The answer is not given.}$

$8192x^{27}$

2x^3

4x^9

4x^6

Correct answer:

$8192x^{27}$

Explanation:

Evaluate h(2x^3) first. Substitute 2x^3 into the function as a replacement of the x-variable.

h(2x^3) = 2(2x^3)^3 = 2(8x^9) = 16x^9

Substitute this value to determine h(h(2x^3)) .

h(h(2x^3)) = h(16x^9) = 2(16x^9)^3=2(16x^9)(16x^9)(16x^9)

The answer is: $8192x^{27}$

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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 : Function Notation

Example Question #21 : Function Notation

Example Question #23 : Function Notation

Example Question #151 : Introduction To Functions

Example Question #21 : Function Notation

Example Question #22 : Function Notation

Example Question #27 : Function Notation

Example Question #28 : Function Notation

Example Question #29 : Function Notation

Example Question #151 : Functions And Graphs

All Algebra II Resources

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