Question

& 17 구 3. Graph g(x) on the coordinate grid below. x +3 x < 4 g(x) = { -2x + 7 , *> 4 5 5 4 4 2 1 -9-9-7-8 5 8 9 x -5 -6 S

Answer 1

We have g(x) that is defined by parts:

`g(x)\begin{cases}x+3,x\le4 \\ -2x+7,x>4\end{cases}`

The first part has a y-intercept at y=3 and a slope of 1.

We can find its value in the limit: at x=4.

`g(4)=x+3=4+3=7`

Then, the point is (4,7).

We can find the x-intercept as:

`\begin{gathered} g(x)=0=x+3 \\ x=-3 \end{gathered}`

So another point of the line is (-3,0).

Drawing a line that passes through those two points will be the graph for x+3.

Then, for g(x) when x>4, the slope is -2 and the y-intercept is 7.

We evaluate the line at x=4, although this point does not belong to the line in this case (as x>4):

`g(4)=-2(4)+7=-8+7=-1`

The point is then (4,-1).

We can calculate another point of the line in order to be able to graph it.

For example, for x=8:

`g(8)=-2(8)+7=-16+7=-9`

The point is then (8,9).

We can now graph both parts of g(x):