Question

course: ap precalculus
segment: 17 - transformations together (d)
question #: 4
due tue, sep 23, 2025
4
find fully expanded formulas for each of the following transformations on y = x² - 5x + 2: 4. stretch the original horizontally by a factor of 3.

Explanation:

Step1: Recall horizontal - stretch rule

For a function $y = f(x)$ stretched horizontally by a factor of $a$, the new function is $y = f(\frac{x}{a})$. Here $a = 3$ and $f(x)=x^{2}-5x + 2$. So the new function is $y=(\frac{x}{3})^{2}-5(\frac{x}{3})+2$.

Step2: Expand the formula

First, expand $(\frac{x}{3})^{2}=\frac{x^{2}}{9}$, and $-5(\frac{x}{3})=-\frac{5x}{3}$. Then $y=\frac{x^{2}}{9}-\frac{5x}{3}+2$.

Answer:

$y=\frac{x^{2}}{9}-\frac{5x}{3}+2$