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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

Example Question #31 : Functions And Graphs

Find the y-intercept of the following equation:

2y=12x+3

Possible Answers:

y=2

x=3

$y=\frac{3}{2}$

$x=\frac{3}{2}$

Correct answer:

$y=\frac{3}{2}$

Explanation:

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

$2y=12x+3\rightarrow 2y=0+3$

Divide both sides by 2 to get y by itself:

$\frac{2y}{2}=\frac{3}{2}$

This gives a final answer of y=3/2

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Example Question #32 : Functions And Graphs

Find the y-intercept of the following equation:

3x-y=12

Possible Answers:

x=-12

x=12

y=-12

y=12

Correct answer:

y=-12

Explanation:

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

$3x-y=12\rightarrow 0-y=12$

Divide both sides by -1 to get y by itself:

$\frac{-1y}{-1}=\frac{12}{-1}$

This gives a final answer of y=-12

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Example Question #33 : Functions And Graphs

Find the y-intercept of the following equation:

y=6x+2

Possible Answers:

x=2

x=6

y=2

y=3

Correct answer:

y=2

Explanation:

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

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

This gives a final answer of y=2

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Example Question #34 : Functions And Graphs

What is the y-intercept of the following equation? 2y-2 = 2x+2

Possible Answers:

$\textup{The equation is not linear.}$

$-\frac{1}{2}$

Correct answer:

Explanation:

Rewrite the equation in slope-intercept form:

y=mx+b

Our objective is to determine the value of , which represents the y-intercept.

Add two on both sides.

2y-2 +(2)= 2x+2+(2)

2y= 2x+4

Divide by 2 on both sides.

$\frac{2y}{2}=\frac{ 2x+4}{2}$

y= x+2

The value of b =2 .

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Example Question #35 : Properties Of Functions And Graphs

What is the y-intercept of the following? y=2(2x-3)^2

Possible Answers:

Correct answer:

Explanation:

The y-intercept is the value of when x=0 .

Substitute the value of x=0 into the given equation.

y=2(2(0)-3)^2 = 2(0-3)^2 = 2(-3)^2 = 2(9)

The answer is:

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Example Question #34 : Functions And Graphs

What is the x-intercept of the equation y= 3x-2 ?

Possible Answers:

$-\frac{3}{2}$

$\frac{3}{2}$

$\frac{2}{3}$

Correct answer:

$\frac{2}{3}$

Explanation:

The x-intercept is the value of x when y=0 .

0= 3x-2

Add two on both sides, and then divide both sides by three.

0+2= 3x-2+2

2=3x

The answer is: $\frac{2}{3}$

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Example Question #34 : Functions And Graphs

Define $h(x)=6- \log _{3}\left ( x-7 \right )$ .

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

Possible Answers:

5.44

4.23

6.56

7.77

The graph of has no -intercept.

Correct answer:

The graph of has no -intercept.

Explanation:

Evaluate h(0) :

$h(x)=6- \log _{3}\left ( x-7 \right )$

$h(0)=6- \log _{3}\left ( 0-7 \right )$

$h(0)=6- \log _{3}\left ( -7 \right )$

A negative number cannot have a logarithm, so h(0) is an undefined expression. Therefore, the graph of has no -intercept.

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Example Question #34 : Properties Of Functions And Graphs

What is the slopeof the line between the points (-1,0) and (3,5)?

Possible Answers:

$\frac{5}{4}$

$\frac{3}{2}$

Correct answer:

$\frac{5}{4}$

Explanation:

For this problem we will need to use the slope equation:

$m=\frac{y_2-y_1}{x_2-x_1}$

In our case (x_1, y_1)=(-1,0) and (x_2, y_2)=(3,5)

Therefore, our slope equation would read:

$m=\frac{5-0}{3--1}=\frac{5}{4}$

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Example Question #1 : Slope

What is the slope of the function

3y=6x-12

Possible Answers:

Correct answer:

Explanation:

To find the slope of this function we first need to get it into slope-intercept form

y=mx+b where m=slope

To do this we need to divide the function by 3:

3y=6x-12

y=2x-4

From here we can see our m, which is our slope equals 2

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Example Question #1 : Slope

What is the slope for the line having the following points: (1, 5), (2, 8), and (3, 11)?

Possible Answers:

Correct answer:

Explanation:

To find the slope for the line that has these points we will use the slope formula with two of the points.

In our case (x_1, y_1)= (1,5) and (x_2, y_2)=(2, 8)

Now we can use the slope formula:

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{8-5}{2-1}=\frac{3}{1}=3$

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All SAT II Math II Resources

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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 #31 : Functions And Graphs

Example Question #32 : Functions And Graphs

Example Question #33 : Functions And Graphs

Example Question #34 : Functions And Graphs

Example Question #35 : Properties Of Functions And Graphs

Example Question #34 : Functions And Graphs

Example Question #34 : Functions And Graphs

Example Question #34 : Properties Of Functions And Graphs

Example Question #1 : Slope

Example Question #1 : Slope

All SAT II Math II Resources

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