### All Algebra II Resources

## Example Questions

### Example Question #11 : Transformations

Transformations

Where will the point be located after the following transformations?

- Reflection about the x-axis
- Translation up 3
- Translation right 4

**Possible Answers:**

**Correct answer:**

Where will the point be located after the following transformations?

- Reflection about the x-axis results in multiplying the y value by negative one thus .
- Translation up 3, means to add three to the y values which results in .
- Translation right 4, means to add four to the x value which will result in .

### Example Question #12 : Transformations

Find the equation of the linear function obtained by shifting the following linear function along the x-axis 3 units to the left. State the y-intercept of .

**Possible Answers:**

y-intercept

y-intercept

y-intercept

y-intercept

y-intercept

**Correct answer:**

y-intercept

The transformation for a left shift along the x-axis for requires we add to the argument of the function .

The y-intercept of the linear function is .

### Example Question #11 : Transformations

If the function is linear and the function is quadratic, then the function is?

**Possible Answers:**

a linear quadratic function

linear function

higher order polynomial function

not a function

quadratic

**Correct answer:**

quadratic

The linear function will have the form,

Where is the y-intercept and is the slope; both are constant.

The quadratic function will have the form,

We are given that the function is defined,

we obtain another function that is also a quadratic function since and are constants. Therefore, is quadratic.

### Example Question #12 : Transformations

Reflect across the x-axis, then reflect across , and then shift this line up five units. What is the new equation?

**Possible Answers:**

**Correct answer:**

Reflect across the x-axis will turn the equation to:

If we then reflect across , the equation will become:

Shifting this line up five units means that we will add five to this equation.

The equation after all the transformations is:

The answer is:

### Example Question #191 : Introduction To Functions

Shift down three units. What is the new equation?

**Possible Answers:**

**Correct answer:**

The equation is currently in standard form. Rewrite the current equation in slope-intercept form. Subtract from both sides.

Since the graph is shifted downward three units, all we need to change is decrease the y-intercept by three. Subtract the right side by three.

The answer is:

### Example Question #711 : Algebra Ii

Reflect the line across the line , and then reflect again across the line . What is the new equation of this horizontal line?

**Possible Answers:**

**Correct answer:**

The distance between and is three units. If the line is reflected across , this means that the new line will also be three units away from .

The equation of the line after this reflection is:

If this line is reflected again across the line , both lines are six units apart, and the reflection would mean that the line below line is also six units apart.

Subtract six from line .

The equation of the line after the transformations is:

The answer is:

### Example Question #13 : Transformations

If the function is shifted down two units and left four units, what is the new y-intercept?

**Possible Answers:**

**Correct answer:**

If the graph was shifted two units down, only the y-intercept will change, and will decrease by two.

The new equation is:

If the graph was shifted left four units, the root will shift four units to the left, and the will need to be replaced with .

The new y-intercept will be .

### Example Question #14 : Transformations

Reflect the line across , and shift the line down three units. What is the new equation?

**Possible Answers:**

**Correct answer:**

The equations with an existing variable is incorrect because they either represent lines with slopes or vertical lines.

After the line is reflected across , the line becomes .

Shifting this line down three units mean that the line will have a vertical translation down three.

Subtract the equation by three.

The result is:

### Example Question #17 : Transformations

Give the equation of the vertical asymptote of the graph of the equation .

**Possible Answers:**

The graph of has no vertical asymptote.

**Correct answer:**

The graph of has no vertical asymptote.

Define . As an exponential function, this has a graph that has no vertical asymptote, as is defined for all real values of . In terms of :

,

The graph of is a transformation of that of - a horizontal shift ( ), a vertical stretch ( ), and a vertical shift ( ) of the graph of ; none of these transformations changes the status of the function as one whose graph has no vertical asymptote.

### Example Question #15 : Transformations

Give the equation of the horizontal asymptote of the graph of the equation

**Possible Answers:**

The graph of has no horizontal asymptote.

**Correct answer:**

Define in terms of ,

It can be restated as the following:

The graph of has as its horizontal asymptote the line of the equation . The graph of is a transformation of that of —a right shift of 2 units , a vertical stretch , and an upward shift of 5 units . The right shift and the vertical stretch do not affect the position of the horizontal asymptote, but the upward shift moves the asymptote to the line of the equation . This is the correct response.