SAT II Math II : Properties of Functions and Graphs

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

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Example Questions

Example Question #1 : X Intercept And Y Intercept

Define .

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

Possible Answers:

The graph of  has no -intercept.

Correct answer:

Explanation:

Set  and solve for :

Example Question #11 : X Intercept And Y Intercept

Define .

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

Possible Answers:

The graph of  has no -intercept.

Correct answer:

The graph of  has no -intercept.

Explanation:

Set  and solve for :

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

The graph of  has no -intercept.

Example Question #21 : Properties Of Functions And Graphs

Define 

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

Possible Answers:

The graph of  has no -intercept.

Correct answer:

Explanation:

Set  and solve for :

Example Question #21 : Functions And Graphs

Define 

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

Possible Answers:

The graph of  has no -intercept.

Correct answer:

Explanation:

Evaluate :

Example Question #14 : X Intercept And Y Intercept

Define .

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

Possible Answers:

The graph of  has no -intercept.

Correct answer:

The graph of  has no -intercept.

Explanation:

Evaluate :

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

Example Question #21 : Functions And Graphs

Find the  intercept of the function. 

Possible Answers:

Correct answer:

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.

Example Question #21 : Functions And Graphs

Find the x-intercept of the following equation:

Possible Answers:

Correct answer:

Explanation:

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

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

This gives a final answer of x=-3

Example Question #22 : Functions And Graphs

Find the x-intercept of the following equation:

Possible Answers:

Correct answer:

Explanation:

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

Divide by 2 to get x by itself:

This gives a final answer of x=6

Example Question #23 : Functions And Graphs

Find the x-intercept of the following equation:

Possible Answers:

Correct answer:

Explanation:

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

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

This gives a final answer of x=4

Example Question #24 : Functions And Graphs

Find the x-intercept of the following equation:

Possible Answers:

Correct answer:

Explanation:

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

Divide by 6 to get x by itself:

This gives a final answer of x=5/6

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