Compare the given linear function to its parent function f(x) and determine the transformations:

g(x) = -1/3f(x) + 5

The new function is (1) and (2) and (3)

(1).
A. Reflected over the x-axis
B. did not reflect over the x-axis

(2)
A. steeper than the parent function
B. less steep than the parent function

(3)
A. shifted up 5 units
B. shifted down 5 units
C. no vertical shift

1 answer

The given linear function is g(x) = -1/3f(x) + 5.

(1) The new function is reflected over the x-axis because of the negative coefficient (-1/3) multiplying f(x). Therefore, the answer is A. Reflected over the x-axis.

(2) The new function is less steep than the parent function because of the absolute value of the fraction in front of f(x), which is 1/3. Since 1/3 is less than 1, the new function is less steep. Therefore, the answer is B. Less steep than the parent function.

(3) The new function is shifted up 5 units because of the constant term added at the end, which is +5. Therefore, the answer is A. Shifted up 5 units.