Question

The function g(x) is a transformation of the cube root parent function,

f(x) = y. What function is g(x)?
5
g(x)
f(x)
5
-5
A. g(x) = 1 va
B. g(x) = a + 2
C. g(x) = 27

Answer 1

g(x) =
`2(\sqrt[3]{x})`

Explanation:

Parent function given in the graph attached is,

f(x) =
`\sqrt[3]{x}`

Function 'f' passes through a point (1, 1).

If the parent function is stretched vertically by 'k' unit,

Transformed function will be,

g(x) = k.f(x)

Therefore, the image of the parent function will be,

g(x) =
`k(\sqrt[3]{x})`

Since, the given function passes through (1, 2)

g(1) =
`k(\sqrt[3]{1})` = 2

⇒ k = 2

Therefore, image of the function 'f' will be,

g(x) =
`2(\sqrt[3]{x})`