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?

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.