Question

For the parent function y=√x what effect does a value of k = -3 have on the graph?

Horizontal shift of 3 units to the right

Horizontal shift of 3 units to the left

Vertical shift of 3 units up

Vertical shift of 3 units down

Answer 1

Vertical shift of 3 units down ⇒ last answer

Explanation:

* Lets revise the translation of a function

- If the function f(x) translated horizontally to the right

by h units, then the new function g(x) = f(x - h)

- If the function f(x) translated horizontally to the left

by h units, then the new function g(x) = f(x + h)

- If the function f(x) translated vertically up

by k units, then the new function g(x) = f(x) + k

- If the function f(x) translated vertically down

by k units, then the new function g(x) = f(x) – k

* Lets solve the problem

∵ The parent function y = √x

∵ There is a translation by k = -3

- From the rules above k is for the vertical translation

∵ k = -3

- That means the parent function translated 3 units down

∴ The value of k = -3 makes the graph of the parent function translated

3 units down

- For more understand look to the attached graph

# y = √x ⇒ the red graph

# y = √x - 3 ⇒ the blue graph