Chapter 6.4, Problem 45PPS

(a)

To determine

To find: Zeroes, x- and y- intercept and turning point

Explanation of Solution

Given information:

The given equation is

  $y=\{\begin{array}{l}{x}^{2}ifx\le -4\\ 5if-4<x\\ x^{3}ifx>0\end{array}\le 0$

Interpretation: Graph for the function $\text{y}= x^2$ for $x\le -\text{4}$ and $\text{x }\le \text{4}$ will be parabolic and then $\text{x}\ge -4$ and $\text{x}\le 0$ graph becomes constant

Therefore, there is break in the graph.

Now, for $\text{y}= x^3$ if, $\text{x}>0$ the graph will be obtained

Therefore the graph of continuity is in possible, so the given function cannot be graphed so, no zeroes and x- intercept and y- intercept.

(b)

To determine

To find: The axis of symmetry.

Answer to Problem 45PPS

There is no line of symmetry

Explanation of Solution

Given information:

The given equation is $y=\{\begin{array}{l}{x}^{2}ifx\le -4\\ 5if-4<x\\ x^{3}ifx>0\end{array}\le 0$

Calculation:

Line of symmetry means the line which makes the given graph into two equal parts.

Therefore, graph is not possible

Therefore, there will be no line of symmetry.

(c)

To determine

To find: The intervals for which it is increasing, decreasing, or constant

Answer to Problem 45PPS

The graph is increasing in the interval $\text{x}\le -0.\text{5}$ and decreasing in $\text{x}<-\text{2}$ and $\text{x}\ge -0.\text{5}$

Explanation of Solution

Given information:

The given equation is $\text{y}=$

  $y=\{\begin{array}{l}{x}^{2}ifx\le -4\\ 5if-4<x\\ x^{3}ifx>0\end{array}\le 0$

Calculation:

From the given distribution of the function it can be said that the function is decreasing in the intervals, $x\le -\text{4}$ and constant in the intervals $-\text{4}<x\le 0$ and increasing in the interval $x>0$

Therefore, the graph is increasing in the interval $x\le -0.\text{5}$ and decreasing in $x<-\text{2}$ and $x\ge -0.\text{5}$