### All Algebra II Resources

## Example Questions

### Example Question #5 : Introduction To Functions

Which analysis can be performed to determine if an equation is a function?

**Possible Answers:**

Horizontal line test

Calculating zeroes

Vertical line test

Calculating domain and range

**Correct answer:**

Vertical line test

The vertical line test can be used to determine if an equation is a function. In order to be a function, there must only be one (or ) value for each value of . The vertical line test determines how many (or ) values are present for each value of . If a single vertical line passes through the graph of an equation more than once, it is not a function. If it passes through exactly once or not at all, then the equation is a function.

The horizontal line test can be used to determine if a function is one-to-one, that is, if only one value exists for each (or ) value. Calculating zeroes, domain, and range can be useful for graphing an equation, but they do not tell if it is a function.

Example of a function:

Example of an equation that is not a function:

### Example Question #1 : Functions As Graphs

Which graph depicts a function?

### Example Question #2 : Functions As Graphs

The graph below is the graph of a piece-wise function in some interval. Identify, in interval notation, the decreasing interval.

**Possible Answers:**

**Correct answer:**

As is clear from the graph, in the interval between ( included) to , the is constant at and then from ( not included) to ( not included), the is a decreasing function.

### Example Question #3 : Functions As Graphs

Without graphing, determine the relationship between the following two lines. Select the most appropriate answer.

**Possible Answers:**

Perpendicular

Intersecting

Complementary

Parallel

Supplementary

**Correct answer:**

Perpendicular

**Perpendicular lines** have slopes that are negative reciprocals. This is the case with these two lines. Although these lines interesect, this is not the most appropriate answer since it does not account for the fact that they are perpendicular.

### Example Question #4 : Functions As Graphs

Find the slope from the following equation.

**Possible Answers:**

**Correct answer:**

To find the slope of an equation first get the equation in slope intercept form.

where,

represents the slope.

Thus

### Example Question #5 : Functions As Graphs

**Possible Answers:**

3 spaces up, 2 spaces left

3 spaces right, 2 spaces up

3 spaces left, 2 spaces down

3 spaces right, 2 spaces down

**Correct answer:**

3 spaces left, 2 spaces down

When determining how a the graph of a function will be translated, we know that anything that happens to x in the function will impact the graph horizontally, opposite of what is expressed in the function, whereas anything that is outside the function will impact the graph vertically the same as it is in the function notation.

For this graph:

The graph will move 3 spaces left, because that is the opposite sign of the what is connected to x directly.

Also, the graph will move down 2 spaces, because that is what is outside the function and the 2 is negative.

### Example Question #6 : Functions As Graphs

Define a function .

Is this function even, odd, or neither?

**Possible Answers:**

Odd

Neither

Even

**Correct answer:**

Odd

To identify a function as even odd, or neither, determine by replacing with , then simplifying. If , the function is even; if is odd.

,

so

By the Power of a Product Property,

,

so is an odd function

### Example Question #7 : Functions As Graphs

Define a function .

Is this function even, odd, or neither?

**Possible Answers:**

Even

Neither

Odd

**Correct answer:**

Neither

To identify a function as even odd, or neither, determine by replacing with , then simplifying. If , the function is even; if is odd.

so

By the Power of a Product Property,

, so is not an even function.

,

, so is not an odd function.

### Example Question #8 : Functions As Graphs

Define a function .

Is this function even, odd, or neither?

**Possible Answers:**

Even

Neither

Odd

**Correct answer:**

Even

To identify a function as even, odd, or neither, determine by replacing with , then simplifying. If , the function is even; if is odd.

, so is an even function.

### Example Question #9 : Functions As Graphs

Define a function .

Is this function even, odd, or neither?

**Possible Answers:**

Odd

Even

Neither

**Correct answer:**

Odd

To identify a function as even, odd, or neither, determine by replacing with , then simplifying. If , the function is even; if is odd.

Since , is an odd function.

Certified Tutor