Use the graph of the function f shown to find:

(a) Find the domain and range of f.

(b) List the intercepts

(c) Find $f(-2)$

(d) Find the value(s) of xfor which $f\left(x\right)=-3$

(e) Solve $f\left(x\right)>0.$

(f) Graph $y=f(x-3)$

(g) Graph $y=f\left(\frac{1}{2}x\right)$

(h) Graph $y=-f\left(x\right)$

The given graph

The points on the graph of f have x-coordinates between -4 and 3 , inclusive. So, for each number x between -4 and 3 , there is a point $(x,f(x\left)\right)$on the graph.

Therefore, the domain of f is $\left\{x|-4\le x\le 3\right\}$ or $[-4,3]$the interval .

The points on the graph of f all have they- coordinates between 3 and -3 , inclusive.
For each value of y between 3 and -3 , there exists at least one number x in the domain.

So, the range of fis $\left\{y|3\le x\le -3\right\}$or the interval$[3,-3]$ .

Intercepts are the points where the graph touches the coordinate axes. Thex-intercepts have the y-coordinates 0, and they-intercepts have thex-coordinates 0.
From the graph we can see that the origin$(0,0)$ is the only intercept.

$f(-2)$is the value ofyon the graph when the value of x is -2 .
The point $(-2,-1)$on the graph corresponds to this situation. Thus, $f(-2)=-1$.

$f\left(x\right)=-3$means that the value of y on the graph is -3 at a given x-value. Look for points on the graph for which the y-coordinate is -3 .

The point$(-4,-3)$on the graph corresponds to this situation.
Thus,$f\left(x\right)=-3$ , when$x=-4$

The function $f\left(x\right)>0$, indicates that the y-coordinate should have positive values for each value of thex-coordinate.
In the graph, x-values from -4 to 3 are shown. Determine for which of these values the y-coordinate is positive.
The points occur on$[0,3]$ .
So, using inequality notations, $f\left(x\right)>0$for $0\le x\le 3$

Since 3 is substracted from $f\left(x\right)$,the graph of $y=f(x-3)$ is obtained by shifting the graph of f horigontally to the right by 3 units

The graph of $f\left(\frac{1}{2}x\right)$is the horizontally compressed versionof the graph of $f\left(x\right)$by a factor of $\frac{1}{2}$.The function $f\left(x\right)$is graphed by multiplaying each x -coordinate of $f\left(x\right)$by $\frac{1}{2}$

The graph of the function $f\left(x\right)$is the reflection of the graph of $f\left(x\right)$ about the y-axis.The function $f\left(x\right)$ is graphed by multiplaying the x -coordinates of $f\left(x\right)$ by -1.