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SAT II Math II : Functions and Graphs

Study concepts, example questions & explanations for SAT II Math II

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Example Questions

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Example Question #10 : X Intercept And Y Intercept

Define $g(x)=5- \log _{4}\left ( x+5 \right )$ .

Give the -coordinate of the -intercept of the graph of .

Possible Answers:

620

1,019

The graph of has no -intercept.

12,495

49,995

Correct answer:

1,019

Explanation:

Set g(x) = 0 and solve for :

$5- \log _{4}\left ( x+5 \right ) = 0$

$\log _{4}\left ( x+5 \right ) = 5$

$x+5 = 4^{5}$

x+5 = 1,024

x=1,019

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Example Question #21 : Functions And Graphs

Define $g(x) = 3 + \sqrt[4]{3x-5}$ .

Give the -coordinate of the -intercept of the graph of .

Possible Answers:

$-28\frac{2}{3}$

$28\frac{2}{3}$

The graph of has no -intercept.

$25\frac{1}{3}$

$-25\frac{1}{3}$

Correct answer:

The graph of has no -intercept.

Explanation:

Set g(x) = 0 and solve for :

$3 + \sqrt[4]{3x-5} = 0$

$\sqrt[4]{3x-5} = -3$

This equation has no solution, since a principal even root of a real number must be positive.

The graph of has no -intercept.

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Example Question #22 : Functions And Graphs

Define $f(x) = 4 + \sqrt[5]{2x-9}$

Give the -coordinate of the -intercept of the graph of (nearest hundredth).

Possible Answers:

$-516\frac{1}{2}$

$-507\frac{1}{2}$

$507\frac{1}{2}$

$516\frac{1}{2}$

The graph of has no -intercept.

Correct answer:

$-507\frac{1}{2}$

Explanation:

Set f(x) = 0 and solve for :

$4 + \sqrt[5]{2x-9} = 0$

$\sqrt[5]{2x-9} = -4$

$\left (\sqrt[5]{2x-9} \right ) ^{5}= \left (-4 \right ) ^{5}$

2x-9 = -1,024

2x= -1,015

$x=-507\frac{1}{2}$

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Example Question #21 : Properties Of Functions And Graphs

Define $f(x) = 2 \cdot 3^{x-4}- 7$

Give the -coordinate of the -intercept of the graph of (nearest hundredth).

Possible Answers:

The graph of has no -intercept.

-7.02

-6.98

-4.42

-5.14

Correct answer:

-6.98

Explanation:

Evaluate f(0) :

$f(x) = 2 \cdot 3^{x-4}- 7$

$f(0) = 2 \cdot 3^{0-4}- 7$

$= 2 \cdot 3^{-4}- 7$

$= 2 \cdot \frac{1}{81}- 7$

$= \frac{2}{81}- 7$

$=-6 \frac{79}{81} \approx -6.98$

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Example Question #21 : Properties Of Functions And Graphs

Find the intercept of the function.

36x^2+16y^2=72

Possible Answers:

$x=\pm0.5$

$x=\pm \sqrt{0.5}$

$x=\pm \sqrt{2}$

x=2

$x=\pm 2$

Correct answer:

$x=\pm \sqrt{2}$

Explanation:

The function will cross the x axis when the y coordinate is equal to zero. To find the x intercept plug in the value zero for y and then solve the equation for x. This will be the x coordinate where the function crosses the x-axis, or the x intercept.

36x^2+16y^2=72

36x^2+16(0)^2=72

36x^2=72

x^2=2

$x=\pm \sqrt{2}$

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Example Question #231 : Sat Subject Test In Math Ii

Find the x-intercept of the following equation:

y=2x+6

Possible Answers:

x=-3

y=-3

y=6

x=2

Correct answer:

x=-3

Explanation:

In order to find the x-intercept, set y=0 then solve for x. For this equation that looks as follows:

$y=2x+6\rightarrow 0=2x+6$

Subtract 2x from both sides, then divide by -2 to get x by itself:

$\frac{-2x}{-2}=\frac{6}{-2}$

This gives a final answer of x=-3

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Example Question #232 : Sat Subject Test In Math Ii

Find the x-intercept of the following equation:

2x+y=12

Possible Answers:

x=6

y=12

x=12

y=6

Correct answer:

x=6

Explanation:

In order to find the x-intercept, set y=0 then solve for x. For this equation that looks as follows:

$2x+y=12\rightarrow 2x+0=12$

Divide by 2 to get x by itself:

$\frac{2x}{2}=\frac{12}{2}$

This gives a final answer of x=6

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Example Question #233 : Sat Subject Test In Math Ii

Find the x-intercept of the following equation:

y=4x-16

Possible Answers:

x=-4

x=4

y=4

y=-16

Correct answer:

x=4

Explanation:

In order to find the x-intercept, set y=0 then solve for x. For this equation that looks as follows:

$y=4x-16\rightarrow 0=4x-16$

Subtract 4x from both sides, then divide by -4 to get x by itself:

$\frac{-4x}{-4}=\frac{-16}{-4}$

This gives a final answer of x=4

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Example Question #241 : Sat Subject Test In Math Ii

Find the x-intercept of the following equation:

2y+6x=5

Possible Answers:

$x=\frac{5}{6}$

x=3

y=3

$x=\frac{6}{5}$

Correct answer:

$x=\frac{5}{6}$

Explanation:

In order to find the x-intercept, set y=0 then solve for x. For this equation that looks as follows:

$2y+6x=5\rightarrow 0+6x=5$

Divide by 6 to get x by itself:

$\frac{6x}{6}=\frac{5}{6}$

This gives a final answer of x=5/6

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Example Question #242 : Sat Subject Test In Math Ii

Find the y-intercept of the following equation:

2x+6y=15

Possible Answers:

$y=\frac{15}{6}$

x=6

x=5

$x=\frac{15}{6}$ y=3

Correct answer:

$y=\frac{15}{6}$

Explanation:

In order to find the y-intercept, set x=0 then solve for y. For this equation that looks as follows:

$2x+6y=15\rightarrow 0+6y=15$

Divide both sides by 6 to get y by itself:

$\frac{6y}{6}=\frac{15}{6}$

This gives a final answer of y=15/6

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SAT II Math II : Functions and Graphs

Study concepts, example questions & explanations for SAT II Math II

All SAT II Math II Resources

Example Questions

Example Question #10 : X Intercept And Y Intercept

Example Question #21 : Functions And Graphs

Example Question #22 : Functions And Graphs

Example Question #21 : Properties Of Functions And Graphs

Example Question #21 : Properties Of Functions And Graphs

Example Question #231 : Sat Subject Test In Math Ii

Example Question #232 : Sat Subject Test In Math Ii

Example Question #233 : Sat Subject Test In Math Ii

Example Question #241 : Sat Subject Test In Math Ii

Example Question #242 : Sat Subject Test In Math Ii

All SAT II Math II Resources

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