GRE Math : Algebraic Functions

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Example Questions

Example Question #2791 : Sat Mathematics

If $\small f(x) = 4x^{2}+3x+2$ and $\small g(x) = x+7$ , what is $\small f(g(x))$ ?

Possible Answers:

$\small 4x^{2}+59x+219$

$\small 4x^{2}+3x+72$

$\small 4x^{2}+17x+219$

$\small 4x^{2}+3x+219$

$\small 4x^{2}+17x+72$

Correct answer:

$\small 4x^{2}+59x+219$

Explanation:

$\small 4(x+7)^{2} +3(x+7)+2$

$\small 4(x^{2} + 14x + 49)+ 3x +21 + 2$

$\small 4x^{2}+56x+196+3x+23$

$\small 4x^{2}+59x+219$

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Example Question #23 : Algebraic Functions

If f(6)=7 and f(10)=17 , which of the following could represent f(x) ?

Possible Answers:

3x - 1

1.5x - 2

2x + 5

x + 4

2.5x - 8

Correct answer:

2.5x - 8

Explanation:

The number in the parentheses is what goes into the function.

For the function f(x) = 2.5x - 8 ,

f(6) = 2.5(6) - 8 = 7 and

f(10) = 2.5(10) - 8 = 17

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Example Question #2792 : Sat Mathematics

A function F is defined as follows:

for x² > 1, F(x) = 4x² + 2x – 2

for x²< 1, F(x) = 4x² – 2x + 2

What is the value of F(1/2)?

Possible Answers:

$\frac{7}{2}$

$\frac{1}{2}$

Correct answer:

Explanation:

For F(1/2), x²=1/4, which is less than 1, so we use the bottom equation to solve. This gives F(1/2)= 4(1/2)² – 2(1/2) + 2 = 1 – 1 + 2 = 2

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Example Question #11 : Algebraic Functions

Which of the statements describes the solution set for –7(x + 3) = –7x + 20 ?

Possible Answers:

There are no solutions.

x = –1

All real numbers are solutions.

x = 0

Correct answer:

There are no solutions.

Explanation:

By distribution we obtain –7x – 21 = – 7x + 20. This equation is never possibly true.

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Example Question #12 : Algebraic Functions

Will just joined a poetry writing group in town that meets once a week. The number of poems Will has written after a certain number of meetings can be represented by the function f(p) = 2p+6 , where represents the number of meetings Will has attended. Using this function, how many poems has Will written after 7 classes?

Possible Answers:

Correct answer:

Explanation:

For this function, simply plug 7 in for and solve:

f(p)=2p+6=2(7)+6=20

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Example Question #13 : Algebraic Functions

If $f(x)=x^{2}+3$ , then $f(x+h)=$ ?

Possible Answers:

$x^{2}+h^{2}$

$x^{2}+2xh+h^{2}$

$x^{2}+2xh+h^{2}+3$

$x^{2}+h^{2}+3$

$x^{2}+3+h$

Correct answer:

$x^{2}+2xh+h^{2}+3$

Explanation:

To find $f(x+h)$ when $f(x)=x^{2}+3$ , we substitute $(x+h)$ for $x$ in $f(x)$ .

Thus, $f(x+h)=(x+h)^{2}+3$ .

We expand $(x+h)^{2}$ to $x^{2}+xh+xh+h^{2}$ .

We can combine like terms to get $x^{2}+2xh+h^{2}$ .

We add 3 to this result to get our final answer.

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Example Question #15 : Algebraic Functions

What is the value of the function f(x) = 6x²+ 16x – 6 when x = –3?

Possible Answers:

–108

–12

Correct answer:

Explanation:

There are two ways to do this problem. The first way just involves plugging in –3 for x and solving 6〖(–3)〗²+ 16(–3) – 6, which equals 54 – 48 – 6 = 0. The second way involves factoring the polynomial to (6x – 2)(x + 3) and then plugging in –3 for x. The second way quickly shows that the answer is 0 due to multiplying by (–3 + 3).

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Example Question #14 : Algebraic Functions

Given the functions f(x) = 2x + 4 and g(x) = 3x – 6, what is f(g(x)) when x = 6?

Possible Answers:

144

192

Correct answer:

Explanation:

We need to work from the inside to the outside, so g(6) = 3(6) – 6 = 12.

Then f(g(6)) = 2(12) + 4 = 28.

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Example Question #15 : Algebraic Functions

A function f(x) = –1 for all values of x. Another function g(x) = 3x for all values of x. What is g(f(x)) when x = 4?

Possible Answers:

–1

–3

–12

Correct answer:

–3

Explanation:

We work from the inside out, so we start with the function f(x). f(4) = –1. Then we plug that value into g(x), so g(f(x)) = 3 * (–1) = –3.

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Example Question #17 : Algebraic Functions

What is f(–3) if f(x) = x² + 5?

Possible Answers:

–4

–14

Correct answer:

Explanation:

f(–3) = (–3)² + 5 = 9 + 5 = 14

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GRE Math : Algebraic Functions

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #2791 : Sat Mathematics

Example Question #23 : Algebraic Functions

Example Question #2792 : Sat Mathematics

Example Question #11 : Algebraic Functions

Example Question #12 : Algebraic Functions

Example Question #13 : Algebraic Functions

Example Question #15 : Algebraic Functions

Example Question #14 : Algebraic Functions

Example Question #15 : Algebraic Functions

Example Question #17 : Algebraic Functions

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