Algebra II : Transformations

Study concepts, example questions & explanations for Algebra II

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Example Questions

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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:

Explanation:

Where will the point  be located after the following transformations?

  1. Reflection about the x-axis results in multiplying the y value by negative one thus .
  2. Translation up 3, means to add three to the y values which results in  .
  3. 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

  

 

Explanation:

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 .  

 

 Plotproblem7

 

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 

Explanation:

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:

Explanation:

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:

 

Explanation:

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:

Explanation:

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:

 

Explanation:

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:

Explanation:

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.

Explanation:

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:

Explanation:

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.

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