Question

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 (g(x) = -1/(x - 5)² - 3). 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)

a. Yes, both equations are correct.
b. No, Sam's equation is incorrect. He made a mistake in the ___________ₛtep.
c. No, Sara's equation is incorrect. She made a mistake in the ___________ₛtep.
d. No, both equations are incorrect.

Answer 1

No, both equations are incorrect. Sam's equation should have had a vertical compression factor of -1/4, and Sara's equation should have had a reflection over the x-axis.

Step-by-step explanation:

No, both equations are incorrect. Sam's equation (g(x) = -4(x+ 5)² - 3) is incorrect because he made a mistake in the compression step. To vertically compress a function by a factor of 4, the equation should have been -1/4*(x+ 5)² - 3. Sara's equation (g(x) = -1/(x - 5)² - 3) is also incorrect because she made a mistake in the reflection step.

To reflect a function over the x-axis, the equation should have been -1/(x - 5)² + 3. The correct transformed function is g(x) = -1/4*(x+ 5)² + 3.