Answers:
The line of symmetry of g(x) is x = 1 ---> False
The maximum of g(x) is less than the maximum of f(x) ---> False
The value of x when f(x) is at its maximum is less than the value of x when g(x) is at its maximum ----> True
Step-by-step explanation:
The line of symmetry of g(x) is the line that divides the graph into two equal parts. In this case, that line is the vertical line x = -1 and since x = -1 and x = 1 are distinct, the first statement is false.
The maximum point of g(x) is the point (-1, 5), so the maximum is 5.
On the other hand, if we have a function y = -(x - h)² + k, the maximum will be the point (h, k) So, the maximum of y will be k. So, for f(x) = -(x + 7)² + 3, the maximum is 3.
Since 5 is greater than 3, we get that the maximum of g(x) is greater than the maximum of f(x) and the second statement is false.
Finally, the value of x when f(x) is at its maximum is -7 and the value of x when g(x) is at its maximum is -1. Then -7 is less than -1 and the third statement is true.