Question

Which of the following options represents the graph of the function show above? f(x) = (x+3) ^3- 1

f(x) = (x-3) ^311
f(x) = (x-3)^3+ 1
f(x) = ( x + 3)^3+1

Answer 1

C

Explanation:

First, notice that this is a cubic function.

The standard form for a cubic function is:

`f(x)=a(x-b)^3+c`

Where a is the vertical stretch, b is the horizontal shift, and c is the vertical shift.

From our graph, we can see that unlike the parent function, x³, this cubic is 3 units to the right and 1 unit up from the standard position.

Therefore, our b is +3 and c is +1. Let's substitute these values. Also, let's assume a is 1. So:

`f(x)=(x-3)^3+1`

Therefore, our answer is C.

And we're done!