Question

Use the given graph of the function f to answer parts (a) – (n).

(a) Find $f\left(0\right)$ and $f\left(6\right)$.

(b) Find $f\left(2\right)$and $f\left(-2\right)$.

(c) Is $f\left(3\right)$positive or negative?

(d) Is $f\left(-1\right)$positive or negative?

(e) For what values of x is $f\left(x\right)=0$?

(f) For what values of x is localid="1650172833683" $f\left(x\right)<0$?

(g) What is the domain of f ?

(h) What is the range of f ?

(i) What are the x-intercepts?

(j) What is the y-intercept?

(k) How often does the line y = -1 intersect the graph?

(l) How often does the line x = 1 intersect the graph?

(m) For what value of x does $f\left(x\right)=3$?

(n) For what value of x does $f\left(x\right)=-2$?

Short answer

(a) $$\begin{gathered} f\left(0\right)=0 \\ f\left(6\right)=0 \end{gathered}$$

(b) localid="1650257857078" $f\left(2\right)=-2andf\left(-2\right)=1$

(c) $f\left(3\right)$is negative

(d) $f\left(-1\right)$is positive

(e) $f\left(x\right)=0$when $x=0,4,6$

(f) $f\left(x\right)<0forx\in \left(0,4\right)$

(g) $D:\left[-4,6\right]$

(h) $R:\left[-2,3\right]$

(i) x-intercepts $\left(0,0\right),\left(4,0\right)and\left(6,0\right)$

(j) y-intercepts is $\left(0,0\right)$

(k) thrice

(l) once

(m) $x=5$

(n) $x=2$

Step-by-step solution

Part (a) Step 1. Given information

Consider the given graph,

Part (a) of Step 1. Find f(0) and f(6)

Using the graph to determine the values we get

$$\begin{gathered} f\left(0\right)=0 \\ f\left(6\right)=0 \end{gathered}$$

Part (b) of Step 1. Find f(2) and f(-2)

When $x=2$, point $\left(2,-2\right)$in on the graph, so $f\left(2\right)=-2$,

similarly when $x=-2$, point$\left(-2,1\right)$so$f\left(-2\right)=1$

Part (c) of Step 1. f(3) is positive or negative

From the graph, we can see that value of $f\left(3\right)$is below the x-axis so$f\left(3\right)$is negative

Part (d) of Step 1. f(-1) positive or negative

From the graph, we can see that the value $f\left(-1\right)$is above the x-axis, so$f\left(-1\right)$is positive

Part (e) of Step 1. Value of x 

From the graph, we can see that the points $\left(0,0\right),\left(4,0\right)and\left(6,0\right)$are on the graph

$f\left(x\right)=0$when$x=0,4,6$

Part (f) of Step 1.  Value of x

To find the values of x for which $f\left(x\right)<0$,

we have to determine the x values for which the y-coordinates are negativelocalid="1650174144258" $f\left(x\right)<0forx\in \left(0,4\right)$

Part (g) of Step 1. Domain

The domain is the region where x exists on the function

$D:\left[-4.6\right]$

Part (h) of Step 1.  Range

The range of a function is the set of all output values of a function.

From the given graph we can see that the range of function f is$R:\left[-2,3\right]$

Part (i) of Step 1. x-intercepts

x-intercepts are those points where $y=0$

From the graph, we have that x-intercepts are points$\left(0,0\right),\left(4,0\right)and\left(6,0\right)$

Part (j) of Step 1. y-intercepts

y-intercepts are points at which $x=0$

From the graph, we can see that y-intercepts is$\left(0,0\right)$

Part (k) of Step 1.  

From the graph, we can notice that the line $y=-1$intersects the provided graph twice.

Part (l) of Step 1.  

From the graph, we can notice that the line$x=1$intersects the graph only once.

Part (m) of Step 1.  value of x

From the graph we can see that when $x=5$then $f\left(5\right)=3$

Therefore$x=5$

Part (n) of Step 1 . Value of x

From the graph we can see that $f\left(x\right)=-2$when$x=2$