Question

Compare the functions below: f(x) = −3 sin(x − π) + 2

g(x) x y
0 8
1 3
2 0
3 −1
4 0
5 3
6 8
h(x) = (x + 7)^2) − 1
Which function has the smallest minimum?

Answer 1

Answer: f(x)

Explanation:

Answer 2

Given:
f(x) = - 3sin(x - π) + 2
h(x) = (x + 7)² - 1

g(x):
x: 0 1 2 3 4 5 6
g(x): 8 3 0 -1 0 3 8

For the range 0 ≤ x ≤ 6,
(a) f(x) takes a minimum value of -3 + 2 = -1, because the minimum value
for the sine function is -1.
(b) g(x) takes a minimum value of -1 according to the given table.
(c) h(x) takes a minimum value of 7^2 - 1 = 48 when x = 0.

A graph of f(x) and g(x) confirms the conclusions.

Answer: Both f(x) and g(x) have minimum values of -1.