Algebra two. Thanks in an advance

Question

Compare the functions shown below: f(x) = 4 sin (2x − π) - 1 g(x) x y -1 6 0 1 1 -2 2 -3 3 -2 4 1 5 6 h(x) = (x − 2)2 + 4 Which function has the smallest minimum y-value? f(x) g(x) h(x) Both f(x) and g(x) have the same minimum y-value.

Answer 1

f(x) = 4sin(2x-pi) - 1

Any sine or cosine function that takes the form y = a*sin(bx + c) + d , since -1 ≤ sin(bx + c) ≤ 1:

-1 ≤ sin(2x - pi) ≤ 1

-4 ≤ 4sin(2x - pi) ≤ 4

-4 - 1 ≤ 4sin(2x - pi) - 1 ≤ 4 - 1

-5 ≤ 4sin(2x - pi) - 1  ≤ 3

Minimum y value = -5

 

g(x) = (-1, 6) (0, 1) (1, -2) (2, -3) (3, -2) (4, 1) (5, 6)

Minimum y value from the points = -3

 

h(x) = (x - 2)^2 + 4

To find the minimum y value sbstitute x = 2 in the above equation.

h(0) = (2 - 2)^2 + 4 =4

Minimum y value = 4

 

So, f(x) has the minimum value and i.e is -5