Question

what is the effect of replacing the graph of the function $f(x)=2x^2 + 3x + 5$ with $f(x + 5)$? choose the correct answer from the choices. the graph of $f(x)$ shifts to the left by 5 units. the graph of $f(x)$ shifts down by 5 units. the graph of $f(x)$ shifts up by 5 units. the graph of $f(x)$ shifts to the right by 5 units.

Explanation:

Step1: Recall horizontal shift rule

For a function $f(x)$, $f(x + h)$ shifts the graph left by $h$ units when $h>0$.

Step2: Apply rule to given function

Here, $h=5>0$, so $f(x+5)$ is $f(x)$ shifted left 5 units.

Answer:

The graph of $f(x)$ shifts to the left by 5 units.