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Transformation

is the changes made from the parent function.

FOR EXAMPLE:

KNOWLEDGE:

1. 

Describe the transformations that have been

                                                  2

applied to the graph of f(x)=x  as well as Domain and Range.

      a) y= f(x+4)+12

 

ANSWER:

 

  1. 12 units up

  2. 4 units to the left

  3. Domain: {x∈R}

  4. Range: {y∈R|y≧12}

 

            2

f(x)=x 

                        2

f(x)=(x+4)+12 

 

 

 

2.

                  

                    x

Let f(x)=8 .

State the transformation that must be applied to f(x)=2f(-x)+10.  Also, state the y-intercept, the equation of asymptote, and the Domain and Range.

 

ANSWER:

  1. Horizontal reflection

  2. 10 units up

  3. Vertical stretch by the factor of 2

  4. Y-intercept: (0, 12)

  5. Asymptote: y=10

  6. Domain: {x∈R}

  7. Range: {y∈R|y≦10}

            x

f(x)=8 

  　　               x

f(x)=2( -8  )+10

3. 

State the transformations that was applied to the parent function, f(x)= sin x along with its Domain and Range.

 

a. f(x)=sin (5x)+7

 

 

 

 

 

 

 

 

 

 

 

 

ANSWER:

  1. Horizontal compressed by the factor of 5

  2. 7 units up

  3. Vertical stretch by the factor of 2

  4. Domain: {x∈R}

  5. Range: {y∈R|6≦y≦10}

 

            

f(x)=sinx 

            

f(x)=sin(5x)+7 

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