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? f(x) g(x) h(x) all three functions have the same minimum value.

We have been given 3 functions and we are asked to determine which of these functions has lowest minimum value.

Let us see the minimum value of each function one by one.

Our first function . We know that range of sin function oscillates between -1 to 1.

The minimum value of the function will occur when value of sine is maximum. Let us see by substituting sin's value 1 in our function.

. So we get -1 as minimum value for f(x).

Our second function is g(x) and we have been given a table of values of g(x). On looking at this table we can see that g(x) also has a minimum value of -1.

Our third function is . We can see this function is always positive except -7. Now let us evaluate this function at -7.

Therefore, we can see all these functions have minimum value equals to -1. So option (d) is the correct choice.

step-by-step explanation: