Chapter 4, Problem 39RE

(a)

To determine

To find: The zeros of the graph. $f\left(x\right)=0$

Answer to Problem 39RE

  $x=-3\text{ and }x=2$

Explanation of Solution

Given: The polynomial function, $y=R\left(x\right)$

  

  $f\left(x\right)=0$ , when the graph touch or cross x -axis.

In graph, clearly see at $x=-3\text{ and }x=2$

(b)

To determine

To find: The value from the graph when $f\left(x\right)>0$ .

Answer to Problem 39RE

  $\left(-3,\infty \right)-\left\{2\right\}$

Explanation of Solution

Given: The polynomial function, $y=R\left(x\right)$

  

  $f\left(x\right)>0$ , when the graph above x -axis.

In graph, clearly see $\left(-3,\infty \right)-\left\{2\right\}$

(c)

To determine

To find: The value from the graph when $f\left(x\right)\le 0$ .

Answer to Problem 39RE

  $\left(-\infty ,3\right]\cup \left\{2\right\}$

Explanation of Solution

Given: The polynomial function, $y=R\left(x\right)$

  

  $f\left(x\right)\le 0$ , when the graph below x -axis.

In graph, clearly see $\left(-\infty ,3\right]\cup \left\{2\right\}$

(d)

To determine

To find: The function of the graph.

Answer to Problem 39RE

  $f\left(x\right)=x^3-x^2-8x+12$

Explanation of Solution

Given: The polynomial function, $y=R\left(x\right)$

  

When graph negative $f\left(x\right)\le 0$ , $\left(-\infty ,3\right]\cup \left\{2\right\}$

When graph positive $f\left(x\right)>0$ , $\left(-3,\infty \right)$

Zeros of polynomial $f\left(x\right)=0$ , $x=-3\text{ and }x=2$

At $x=2$ graph touches x-axis it means repeated root.

y -intercept: $\left(0,12\right)$

This is cubic polynomial, $f\left(x\right)=x^3-x^2-8x+12$