Question

The equation below represents the function p.

Answer 1

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.