Question

Please help!! Will give medal!!

Compare the following functions:
(see attachment)
Which function has the smallest minimum?
A. All three functions have the same minimum
B. f(x)
C. g(x)
D. h(x)

Answer 1

The minimum value for f(x) is pretty straight-forward. -5+2=-3

We can tell by looking at the graph of g(x) that its minimum is -2

By symmetry the table shows a minimum of 3

So f(x) has the smallest minimum.

Answer 2

Explanation:

We are given three functions and we have to find which one has the smallest minimum.

I function is

`f(x) = -5sin(2x-\pi) +2`

Since sine varies from -1 to 1, we get this function has a minimum when sine takes value 1.

Minimum of f(x) =1(-5)+2 =-3

II function is

a graph of parabola with minimum at x=3 and y =-2

III function is shown in tabular form.

From the table we find that minimum is x=1 y=3

Tabulating we have

f(x) (3pi/4, -3)

g(x) (3,-2)

h(x) (1,3)

Smallest is for f(x) with least value of -3