Question

question 14 of 45
the point $(3, 27)$ is labeled on the graph of $f(x)=x^3$ in the given standard $(x, y)$ coordinate plane. the graph of $f(x)$ will be translated 3 coordinate units to the left. which of the following points will be on the image of the graph after the translation?
a $(0, 27)$
b $(3, 24)$

Explanation:

Step1: Understand horizontal left translation

For a horizontal translation of $h$ units left, the new function is $f(x+h)$, so the $x$-coordinate of a point $(x,y)$ becomes $x-h$.

Step2: Apply translation to the point

Original point: $(3, 27)$. Translate 3 units left: subtract 3 from the $x$-coordinate.
$3 - 3 = 0$, $y$-coordinate stays 27.

Answer:

A. (0, 27)