Question

I need help with this last problem. Algebra 2

Answer 1

g(x) = (x-2) ^ 1/3 +5

Explanation:

f(x) = x^1/3

We want to shift it 2 units to the right

h(x) = f(x+c) where c<0 to move it to the right

To move it 2 units to the right c =-2

h(x) = f(x-2)

Substitute x-2 in for x in the function

h(x) = (x-2) ^ 1/3

Now we want to shift it 5 units up

g(x) = h(x)+c where c>0 to move it up

To move it 5 units up c =5

g(x) = h(x)+5

g(x) = (x-2) ^ 1/3 +5

Answer 2

\sqrt[3]{x-2} +5 is your answer

Explanation:

A horizontal translation is inside the function is inside the function. Vertical translations are outside the function. A translation to the right would be
`\sqrt[3]{x-2}`. After that that traslation up would be
`\sqrt[3]{x-2} +5`