Question

shifting the cubic function quick check
the point (4, 64) is on the graph of $f(x) = x^3$. what is the point (4, 64) shifted to when $g(x) = f(x) + 8$
(1 point)
\bigcirc (-4, 72)
\bigcirc (72, 4)
\bigcirc (4, 72)
\bigcirc (4, 58)

Explanation:

Step1: Understand the transformation

The function \( g(x) = f(x) + 8 \) represents a vertical shift of the function \( f(x) \). For a function transformation of the form \( y = f(x) + k \), when \( k>0 \), the graph shifts up by \( k \) units. Here, \( k = 8 \), so we shift the \( y \)-coordinate of the point on \( f(x) \) up by 8.

Step2: Apply the transformation to the point

We have the point \( (4, 64) \) on \( f(x) \). For \( g(x) \), the \( x \)-coordinate remains the same (since it's a vertical shift, horizontal coordinates don't change), and we add 8 to the \( y \)-coordinate. So the new \( y \)-coordinate is \( 64 + 8 = 72 \), and the \( x \)-coordinate is still 4. So the new point is \( (4, 72) \).

Answer:

\( (4, 72) \) (corresponding to the option with this point, e.g., if the options are as given, the correct one is the option with \( (4, 72) \))