Question

what is the effect of replacing the graph of the function $f(x)=x^3 - 2x^2 + x + 5$ with $f(x)-3$? choose the correct answer from the choices. the graph of $f(x)$ shifts up by 3 units. the graph of $f(x)$ shifts down by 3 units. the graph of $f(x)$ shifts to the right by 3 units. the graph of $f(x)$ does not move.

Explanation:

Step1: Identify vertical transformation rule

For a function $f(x)$, $f(x) - k$ shifts the graph down $k$ units.

Step2: Match to given modification

Here, $k=3$, so $f(x)-3$ shifts $f(x)$ down 3 units.

Answer:

The graph of $f(x)$ shifts down by 3 units.