Chapter 4.4, Problem 51E

To determine

To match: the function $f\left(x\right)=\left(x-2\right)\left(x-3\right)\left(x+1\right)$ with its graph.

Answer to Problem 51E

The function $f\left(x\right)=\left(x-2\right)\left(x-3\right)\left(x+1\right)$ matches with the graph (D).

Explanation of Solution

Given information:

Given graphs are:

  $f\left(x\right)=\left(x-2\right)\left(x-3\right)\left(x+1\right)$

Calculation:

Consider the given function.

Zeros of the function can be found by

  $\begin{array}{l}f\left(x\right)=\left(x-2\right)\left(x-3\right)\left(x+1\right)=0\\ x=2,x=3,x=-1\end{array}$

Therefore, the graph crosses $x$ axis at $x=2,x=3,x=-1$ .

The graph of D crosses the $x$ axis at $x=2,x=3,x=-1$ .

Hence, the given function matches with the graph (D).