Question

Find the domain and range, the x-intercepts (if any), y-intercepts (if any), intervals on which the function is increasing, decreasing or constant; and the missing function values, indicated by question marks, below each graph

Answer 1

$Domain:(-\infty,\infty)$

$Range:\lbrack-2,2\rbrack$

$\begin{gathered} y-intercept:(0,0) \\ x-\imaginaryI ntercept:(0,0) \end{gathered}$$\begin{gathered} increasing\text{ .\lparen-2,2\rparen} \\ constan\text{ :\lparen-}\infty,-2\rbrack\cup\lbrack2,\infty) \end{gathered}$$\begin{gathered} f(-9)=-2 \\ f(14)=2 \end{gathered}$Explanation

Step 1

a)Domain:The domain of a function is the set of all possible inputs for the function, it means all the x-values the function takes

we can see the x values go fromnegative infinite to positive infinite, hence

$Domain:(-\infty,\infty)$

b)Range:The range of a function is the complete set of all possible resulting values of the dependent variable(y), so again, let's check the graph

therefore,

$Range:\lbrack-2,2\rbrack$

Step 2

intercepts:

a) x-intercept is he x-intercept is where a line crosses the x-axis

and

b) y-intercept is the point where the graph intersects the y-axis

so, let's check those points in the graph

therefore,

$\begin{gathered} y-intercept:(0,0) \\ x-\imaginaryI ntercept:(0,0) \end{gathered}$

Step 3

Increasing, decreasing or constant

a)increasing.A function is increasing if the y y values continuously increase as the x x values increase,

and

b) if the function is constant the graph will look like a horizontal line, so

therefore,

$\begin{gathered} increasing\text{ .\lparen-2,2\rparen} \\ constan\text{ :\lparen-}\infty,-2\rbrack\cup\lbrack2,\infty) \end{gathered}$

Step 4

finally, evaluate the funcion at the indicated poitns:

to do, that check the y coordinate of the indicated x values:

as the function is constant, we have

$\begin{gathered} f(-9)=-2 \\ f(14)=2 \end{gathered}$

I hope this helps you