Graph g(x)=|x−4|+3 .

use the ray tool and select two points to graph each ray.

(0, 7) and (4, 3) for the left-hand ray

(4, 3) and (8, 7) for the right-hand ray

Step-by-step explanation:

(1) Select the points for graphing

(a) y-Intercept

g(x) = |0 - 4| + 3 = |-4| + 3 = 4 + 3 = 7

There is a y-intercept at (7, 0).

(b) x-intercept

0 = |x − 4| + 3

Subtract 3 from each side     -3 = |x - 4|

Impossible. There is no x-intercept.

(c) Minimum

g(x) has a minimum when the absolute term equals zero.

|x - 4| = 0

x - 4  = 0

Add 4 to each side     x = 4

                                g(x) = 0 + 3

                                g(x) = 3

There is a minimum at (4, 3).

Choose (0, 7) and (4, 3) for the left-hand ray.

Let x = 8.

g(x) =|8 - 4| + 3 = |4| + 3 = 4 + 3 = 7

Choose (4, 3) and (8, 7) for the right-hand ray.

(2) Plot your points

Draw markers (dots?) at the coordinates of each point.

(3) Draw the graph

Draw a smooth line through the points.

Extend the rays to the edges of the plot area.

Your graph should look like the figure below.

7

step-by-step explanation: