Question

Which graph represents y = ^3 radical x - 5 ?
PLEASE ANSWER FAST IM TIMED

Answer 1

Answer: Fourth graph

Explanation:

The given function is
`y=\sqrt[3]{x-5}`

To find the x intercept of the graph, put y=0, we get

`0=\sqrt[3]{x-5}\\\\\Rightarrow x-5=0\\\\\Rightarrow\ x=5`

We we look in the given graphs only in the fourth graph the curve is passing through x intercept (5,0) .

Therefore, the fourth graph represents
`y=\sqrt[3]{x-5}`.

Answer 2

The graph of the parent cube root function which is
`y= \sqrt[3]{x}` passes from the origin. We have to find the graph of
`y=\sqrt[3]{x-5}`

Addition or subtraction of a number from the function argument i.e. x, shifts the graph horizontally. Addition of a number to the arguments moves it to left, while subtraction of a number moves it to right. 5 is being subtracted from the function argument x. This means the graph of parent cube root function will be shifted 5 units to the left without any change in the vertical direction.

The final picture shows such a graph. So the correct answer is option D