Answer:
(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.
