Plz help :( 4. Use the facts and graph below to write the equation for g(x).

FACTS

• This graph shows g(x).

• It looks like the graph of the parent function f(x) = x2. However:

o It has been reflected (flipped) over the x-axis.

o It has been shifted down 4 units.

o It has been shifted left 1 unit.

Step 1: Start with the equation f(x) = x2. Write the equation for the graph of g(x) that has been reflected, or flipped, over the x-axis. (2 points)

Step 2: Use the equation you wrote in Step 1. Write the equation for the graph of g(x) that has also been shifted down 4 units. (2 points)

Step 3: Use the equation you wrote in Step 2. Write the equation for the graph of g(x) that has also been shifted left 1 unit. (2 points)

5. Answer the questions below with the correct function, h(x) or k(x), and an explanation. (10 points: 2 points each)

Linear Quadratic

Parent function f(x) = x f(x) = x2

Transformed function h(x) = –2(x + 3) – 7 k(x) = (3x – 5)2 + 1

a. Which function was shifted up from its parent function? How do you know?

b. Which function was shifted left from its parent function? How do you know?

c. Which function involves a reflection of its parent function over the x-axis? How do you know?

d. Which function involves a vertical compression of its parent function? How do you know?

e. Which function involves a horizontal compression of its parent function? How do you know?

6. Sam and Sara each wrote an equation for a function that underwent these transformations from f(x) = x2:

1. Reflected over the x-axis

2. Vertically compressed by a factor of 4

3. Shifted left 5 units

4. Shifted down 3 units

Sam's equation is g(x) = –4(x + 5)2 – 3. Sara's equation is . Is either equation correct? If either student made a mistake, identify the step and explain what they should have done. What is the correct transformed function? (6 points)

7. The function f(x) = x2 undergoes two transformations:

• Reflection over the x-axis

• Shift down 3 units

Does it matter in which order these transformations are done? Write an equation for each to find out. Remember to multiply the entire right side by –1 to reflect it over the x-axis. Simplify your equations as much as possible. (5 points)

a. Write an equation for g(x) by doing the reflection first. (2 points)

i. Reflection only: g(x) =

ii. Reflection then shift: g(x) =

b. Write an equation for h(x) by doing the shift first. (2 points)

i. Shift only: h(x) =

ii. Shift then reflection: h(x) =

c. Does the order of transformations make a difference? (1 point)