Candice wrote the four equations below she examined them, without solving them, to determine which equation has a infinite numbe
r of solutions
2 answers:
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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:
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.
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:
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.