Step-by-step explanation for each question:
For Question 6, the range of a function is all the possible outputs of the function. Since the function can only take the inputs 0, 4, and 7, we can just plug in each into the formula and find their corresponding outputs.
g(0) = 0² - 9 = 0 - 9 = -9
g(4) = 4² - 9 = 16 - 9 = 7
g(7) = 7² - 9 = 49 - 9 = 40
Therefore the only possible outputs of function g, or the range, is {-9, 7, 40}.
For question 4, the input t is a given time, and h(t) is the height of the football at that time.
Hence, h(2.5) is the height of the football (in feet) at 2.5 seconds. The value 2.5 can be plugged into the function [tex]-16t^2+58t+2[/tex] to get the height. This gives us
[tex]-16(2.5)^2 + 58(2.5) + 2[/tex]
[tex]-16(6.25) + 58(2.5) + 2[/tex] [Squaring 2.5]
[tex]-100 + 145 + 2[/tex] [Multiplying]
[tex]47[/tex] [Combining all terms]
We find that the height of the football at 2.5 seconds is 47 feet.
For Question 5, the table of values show all the possible values x can be (or the domain), and what the output of the function f(x) would give for each.
A) f(-3) = 5, as the row with -3 for x has -5 for y.
B) f(0) = 0, as the row with 0 for x has 0 for y.
C) f(1) = -3, as the row with 1 for x has -3 for y.
