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ACT Math : Algebraic Functions

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Example Questions

Example Question #2791 : Sat Mathematics

If 7y = 4x - 12, then x =

Possible Answers:

(7y+12)/3

(7y+12)/4

(7y+3)/12

(7y-12)/4

Correct answer: (7y+12)/4

Explanation:

Adding 12 to both sides and dividing by 4 yields (7y+12)/4.

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Example Question #2 : How To Find F(X)

f(x) = x^2 + 32x -12

What is f(4) ?

Possible Answers:

144

130

156

128

132

Correct answer:

132

Explanation:

f(x) = x^2 + 32x -12

f(4) = 4^2 + 32(4) -12

= 16 + 128 -12

= 132

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Example Question #2791 : Sat Mathematics

If F(x) = 2x² + 3 and G(x) = x – 3, what is F(G(x))?

Possible Answers:

2x²

2x² + 12x +18

6x² + 5x

2x² – 12x +21

6x² – 12x

Correct answer:

2x² – 12x +21

Explanation:

A composite function substitutes one function into another function and then simplifies the resulting expression. F(G(x)) means the G(x) gets put into F(x).

F(G(x)) = 2(x – 3)² + 3 = 2(x² – 6x +9) + 3 = 2x² – 12x + 18 + 3 = 2x² – 12x + 21

G(F(x)) = (2x² +3) – 3 = 2x²

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Example Question #21 : Algebraic Functions

If a(x) = 2x³+ x, and b(x) = –2x, what is a(b(2))?

Possible Answers:

503

128

132

–132

–503

Correct answer:

–132

Explanation:

When functions are set up within other functions like in this problem, the function closest to the given variable is performed first. The value obtained from this function is then plugged in as the variable in the outside function. Since b(x) = –2x, and x = 2, the value we obtain from b(x) is –4. We then plug this value in for x in the a(x) function. So a(x) then becomes 2(–4³) + (–4), which equals –132.

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Example Question #2792 : Sat Mathematics

Let F(x) = x³ + 2x² – 3 and G(x) = x + 5. Find F(G(x))

Possible Answers:

x³ + 17x² + 95x + 172

x³ + 2x² – x – 8

x³ + x² + 2

x³ + 2x² + x + 2

x³ + x² + x + 8

Correct answer:

x³ + 17x² + 95x + 172

Explanation:

F(G(x)) is a composite function where the expression G(x) is substituted in for x in F(x)

F(G(x)) = (x + 5)³ + 2(x + 5)² – 3 = x³ + 17x² + 95x + 172

G(F(x)) = x³ + x² + 2

F(x) – G(x) = x³ + 2x² – x – 8

F(x) + G(x) = x³ + 2x² + x + 2

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Example Question #3 : How To Find F(X)

What is the value of xy²(xy – 3xy) given that x = –3 and y = 7?

Possible Answers:

2881

–6174

3565

–2881

Correct answer:

–6174

Explanation:

Evaluating yields –6174.

–147(–21 + 63) =

–147 * 42 = –6174

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Example Question #21 : Algebraic Functions

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

$g(x)=x-4$

Find $g(f(2))$ .

Possible Answers:

$\dpi{100} \small 2$

$\dpi{100} \small 6$

$\dpi{100} \small 1$

$\dpi{100} \small 4$

$\dpi{100} \small 3$

Correct answer:

$\dpi{100} \small 2$

Explanation:

$g(f(2))$ is $\dpi{100} \small 2$ . To start, we find that $f(2)=2^{2}+2=4+2=6$ . Using this, we find that $g(6)=6-4=2$ .

Alternatively, we can find that $g(f(x))=(x^{2}+2)-4=x^{2}-2$ . Then, we find that $g(f(2))=2^{2}-2=4-2=2$ .

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Example Question #4 : How To Find F(X)

It takes no more than 40 minutes to run a race, but at least 30 minutes. What equation will model this in m minutes?

Possible Answers:

$\left | m-35 \right |> 5$

$\left | m+35 \right |< 5$

$\left | m-35 \right |= 5$

$\left | m-35 \right |< 5$

$\left | m+35 \right |> 5$

Correct answer:

$\left | m-35 \right |< 5$

Explanation:

If we take the mean number of minutes to be 35, then we need an equation which is less than 5 from either side of 35. If we subtract 35 from $m$ minutes and take the absolute value, this will give us our equation since we know that the time it takes to run the marathon is between 30 and 40 minutes.

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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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ACT Math : Algebraic Functions

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #2791 : Sat Mathematics

Example Question #2 : How To Find F(X)

Example Question #2791 : Sat Mathematics

Example Question #21 : Algebraic Functions

Example Question #2792 : Sat Mathematics

Example Question #3 : How To Find F(X)

Example Question #21 : Algebraic Functions

Example Question #4 : How To Find F(X)

Example Question #2791 : Sat Mathematics

Example Question #23 : Algebraic Functions

All ACT Math Resources

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