# SAT II Math I : Graphing Other Functions

## Example Questions

### Example Question #131 : Functions And Graphs

Simplify the following expression:

Possible Answers:

Correct answer:

Explanation:

To simplify, we must first simplify the absolute values.

Now, combine like terms:

### Example Question #2 : Graphing Polynomial Functions

Where does cross the axis?

Possible Answers:

5

-7

7

-3

3

Correct answer:

7

Explanation:

crosses the axis when equals 0. So, substitute in 0 for :

### Example Question #1 : Graphing Other Functions

Which of the following is an equation for the above parabola?

Possible Answers:

Correct answer:

Explanation:

The zeros of the parabola are at  and , so when placed into the formula

each of their signs is reversed to end up with the correct sign in the answer. The coefficient can be found by plugging in any easily-identifiable, non-zero point to the above formula. For example, we can plug in  which gives

### Example Question #1 : Understand Linear And Nonlinear Functions: Ccss.Math.Content.8.F.A.3

Which equation best represents the following graph?

Possible Answers:

None of these

Correct answer:

Explanation:

We have the following answer choices.

The first equation is a cubic function, which produces a function similar to the graph. The second equation is quadratic and thus, a parabola. The graph does not look like a prabola, so the 2nd equation will be incorrect. The third equation describes a line, but the graph is not linear; the third equation is incorrect. The fourth equation is incorrect because it is an exponential, and the graph is not an exponential. So that leaves the first equation as the best possible choice.

### Example Question #31 : Polynomial Functions

Which of the graphs best represents the following function?

Possible Answers:

None of these

Correct answer:

Explanation:

The highest exponent of the variable term is two (). This tells that this function is quadratic, meaning that it is a parabola.

The graph below will be the answer, as it shows a parabolic curve.

### Example Question #7 : Graphing Polynomial Functions

Which of the following is a graph for the following equation:

Possible Answers:

Cannot be determined

Correct answer:

Explanation:

The way to figure out this problem is by understanding behavior of polynomials.

The sign that occurs before the  is positive and therefore it is understood that the function will open upwards. the "8" on the function is an even number which means that the function is going to be u-shaped. The only answer choice that fits both these criteria is:

### Example Question #1 : Graphing Other Functions

Define a function .

for exactly one real value of  on the interval .

Which of the following statements is correct about ?

Possible Answers:

Correct answer:

Explanation:

Define . Then, if , it follows that .

By the Intermediate Value Theorem (IVT), if  is a continuous function, and  and  are of unlike sign, then  for some . As a polynomial,  is a continuous function, so the IVT applies here.

Evaluate  for each of the following values:

Only in the case of  does it hold that  assumes a different sign at both endpoints - . By the IVT, , and , for some .