Match each function to how its graph is related to the graph of the parent function f(x)=^3гxa. the graph of the parent function is shifted 7 units down. b. the graph of the parent function is shifted 7 units rightc. the graph of the parent function is shifted 7 units upd. the graph of the parent function is shifted 7 units left

g(x) = ∛x + 7⇒the graph of the parent function is shifted 7 units up(c)

g(x) = ∛x - 7⇒the graph of the parent function is shifted 7 units down(a)

g(x) = ∛(x - 7)⇒the graph of the parent function is shifted 7 units right(b)

g(x) = ∛(x + 7)⇒the graph of the parent function is shifted 7 units left(d)

Step-by-step explanation:

* Lets revise some transformation

- 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

* Now lets solve the problem

a) ∵ f(x) = ∛x

∵ The graph of the parent function is shifted 7 units down

- Subtract f(x) by 7

∴ g(x) = ∛x - 7

b) ∵ f(x) = ∛x

∵ The graph of the parent function is shifted 7 units right

- The x-coordinate is changed to x - 7

∴ g(x) = ∛(x - 7)

c) ∵ f(x) = ∛x

∵ The graph of the parent function is shifted 7 units up

- Add f(x) by 7

∴ g(x) = ∛x + 7

d) ∵ f(x) = ∛x

∵ The graph of the parent function is shifted 7 units left

- The x-coordinate is changed to x + 7

∴ g(x) = ∛(x + 7)

1.85

Step-by-step explanation:

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