Question

The graph of a function

y = g(x)

on the domain

−8 ≤ x ≤ 8

consists of line segments and semicircles of radius 2 connecting the points

(−8, 0), (−4, 4), (0, 4), (4, 4), (8, 0).

(a) What is the range of g?

0 < y < 60 ≤ y ≤ 4    0 ≤ y ≤ 20 < y < 40 ≤ y ≤ 6

(b) Where is the function increasing? (Select all that apply.)

−8 ≤ x ≤ −2−2 ≤ x ≤ 22 ≤ x ≤ 44 ≤ x ≤ 8−8 ≤ x ≤ 8

Where is the function decreasing? (Select all that apply.)

−8 ≤ x ≤ −2−2 ≤ x ≤ 22 ≤ x ≤ 44 ≤ x ≤ 8−8 ≤ x ≤ 8

(c) Find the multipart formula for y = g(x) if

		if −8 ≤ x ≤ −4
		if −4 ≤ x ≤ 0
		if 0 ≤ x ≤ 4
		if 4 ≤ x ≤ 8

(d) If we restrict the function to the smaller domain

−6 ≤ x ≤ 0,

what is the range?

0 ≤ y ≤ 62 ≤ y ≤ 6    0 ≤ y ≤ 42 ≤ y ≤ 40 ≤ y ≤ 2

(e) If we restrict the function to the smaller domain

0 ≤ x ≤ 4,

what is the range?

2 ≤ y ≤ 40 ≤ y ≤ 2    0 ≤ y ≤ 64 ≤ y ≤ 60 ≤ y ≤ 4

Answer 1