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 [tex]f(x)=-3sin(x-\pi)+2[/tex]. 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.
[tex]f(x)=-3(1)+2=-1[/tex]. 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 [tex]h(x)=(x+7)^{2}-1[/tex]. We can see this function is always positive except -7. Now let us evaluate this function at -7.
[tex]h(x)=(-7+7)^{2}-1=(0)^{2}-1=-1[/tex]
Therefore, we can see all these functions have minimum value equals to -1. So option (d) is the correct choice.
