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 #41 : Functions And Graphs

What is the slope of the function:

Possible Answers:

3

2

4

8

Correct answer:

4

Explanation:

For this question we need to get the function into slope intercept form first which is

 where the m equals our slope.

In our case we need to do algebraic opperations to get it into the desired form

Therefore our slope is 4

Example Question #251 : Sat Subject Test In Math Ii

Find the slope of the following equation:

Possible Answers:

Correct answer:

Explanation:

To find the slope for a given equation, it needs to first be put into the "y=mx+b" format. Then our slope is the number in front of the x, or the "m". For this equation this looks as follows:

First subtract 2x from both sides:

                

That gives us the following:

Divide all three terms by three to get "y" by itself:

This means our "m" is -2/3

Example Question #1 : Slope

Find the slope of the following equation:

Possible Answers:

Correct answer:

Explanation:

To find the slope for a given equation, it needs to first be put into the "y=mx+b" format. Then our slope is the number in front of the x, or the "m". For this equation this looks as follows:

First add x to both sides:

                

That gives us the following:

Divide all three terms by four to get "y" by itself:

This means our "m" is 1/4

Example Question #1 : Slope

Find the slope of the following equation:

Possible Answers:

Correct answer:

Explanation:

To find the slope for a given equation, it needs to first be put into the "y=mx+b" format. Then our slope is the number in front of the x, or the "m". For this equation this looks as follows:

Our equation is already in the "y=mx+b" format, so our "m" is 6.

Example Question #2 : Slope

Find the slope of the following equation:

Possible Answers:

Correct answer:

Explanation:

To find the slope for a given equation, it needs to first be put into the "y=mx+b" format. Then our slope is the number in front of the x, or the "m". For this equation this looks as follows:

To put our equation in the "y=mx+b" format, flip the two terms on the right side of the equation:

So our "m" in this case is -2.

Example Question #1 : Slope

Find the slope given the equation:   

Possible Answers:

Correct answer:

Explanation:

Subtract  on both sides.

Simplify both sides.

Divide by negative 6 on both sides.

The slope is:  

Example Question #1 : Slope

Find the slope of the equation:  

Possible Answers:

Correct answer:

Explanation:

To determine the slope, we need the equation in slope intercept form.

Multiply by four on both sides to eliminate the fraction.

Add  on both sides.

Combine like-terms.

Divide by nine on both sides.

The value of , or the slope, is .

Example Question #11 : Slope

Given the points  and , what is the slope?

Possible Answers:

Correct answer:

Explanation:

Write the slope equation.

Substitute the points and solve for the slope.

The answer is:  

Example Question #1 : Maximum And Minimum

What is the vertex of ?  Is it a max or min?

Possible Answers:

Correct answer:

Explanation:

The polynomial is in standard form of a parabola.

To determine the vertex, first write the formula.

Substitute the coefficients.

Since the  is negative is negative, the parabola opens down, and we will have a maximum.

The answer is:  

Example Question #41 : Properties Of Functions And Graphs

Given the parabola equation , what is the max or minimum, and where?

Possible Answers:

Correct answer:

Explanation:

The parabola is in the form:  

The vertex formula will determine the x-value of the max or min.  Since the value of  is negative, the parabola will open downward, and there will be a maximum.

Write the vertex formula and substitute the correct coefficients.

Substitute this value back in the parabolic equation to determine the y-value.

The answer is:  

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