Question

Stuck on this one please helpA. End Behavior B. Y-interceptC. X-interceptD. DomainE. Range

Answer 1

Given: Graph of a polynomial m(x) is given.

Required: To determine

A. End behavior

B. Y-intercept

C. X-intercept

D. Domain

E. Range

Explanation: The end behavior of a graph is determined by examining the function's graph as it moves to the positive x-axis and the negative x-axis. From the graph given, we can see that

`\begin{gathered} x\rightarrow+\infty,f(x)\rightarrow+\infty\text{ and } \\ x\rightarrow-\infty,f(x)\rightarrow+\infty \end{gathered}`

The y-intercept is the point on the y-axis where the graph cuts the y-axis—the graph given cuts the y-axis at (0,0). Hence the y-intercept is (0,0).

Similarly, the x-intercept is the point where the graph cuts the x-axis. From the given graph, the function cuts the x-axis at (-4,0), (-3,0), (0,0) and (2,0).

The domain is the x-values of the function. Since the given graph attains all the real values on the x-axis. Hence, the function's domain is the set of all the Real values.

`Domain=(-\infty,+\infty),\lbrace x:x\in R\rbrace`

The range represents the set of possible values the function can have for the given x values or domain. From the graph, we can see that the function minimum value is -21 and can have a maximum value of infinity. Hence the range of the function is-

`Range=[-21,+\infty),\lbrace y:-21\leq y<\infty\rbrace`

Final Answer:

A) End behavior

B) Y-intercept=(0,0)

C) X-intercept=(-4,0),(-3,0),(0,0),(2,0)

D) Domain=

`\begin{equation*} (-\infty,+\infty),\lbrace x:x\in R\rbrace \end{equation*}`

E) Range=

`\begin{equation*} [-21,+\infty),\lbrace y:-21\leq y<\infty\rbrace \end{equation*}`