The equation below represents the function p. the graph below represents the function q. complete the following sentences to compare the end behavior of the two functions. 1 tablet option are: less than grather than the same as 2 tablet option are: grather than the same as less than

Answers:

1)Tthe first answer is that as x increases the value of  p(x) approaches a number that is greater than  q (x).

2) the y-intercept of the function p is greater than the y-intercept of the function q.

Explanation:

1) Value of the functions as x increases.

Function p:

p(x)= [ 2/5 ] ˣ - 3

As x increases, the value of the function is the limit when x → ∞.

Since [2/5] is less than 1, the limit of [2/5]ˣ when x → ∞ is 0, and the limit of p(x) is 0 - 3 =  -3.

While in the graph you see that the function q has a horizontal asymptote that shows that the limit of q (x) when x → ∞ is - 4.

Then, the first answer is that as x increases the value of  p(x) approaches a number that is greater than  q (x).

2) y - intercepts.

i) To determine the y-intercept of the function p(x), just replace x = 0 in the equation:

p(x) = [ 2 / 5]⁰ - 3 = 1 - 3 = - 2

ii) The y-intercept of q(x) is read in the graph. It is - 3.

Then the answer is that the y-intercept of the function p is greater than the y-intercept of the function q.