1 A. Mark is researching wireless phone plans. Company A offers a plan that cost

Question

1 A.

Mark is researching wireless phone plans. Company A offers a plan that costs $40 per month plus $.20 per text message sent or received. Company B offers a comparable plan that costs $60 per month but offers unlimited text messaging.

(a) State a linear function f(x) that represent’s Company A’s total charge per month for x amount of texts.

(b) State a linear function g(x) that represent’s Company B’s total charge per month.

(c) If Mark averages 120 texts sent and received per month, which plan would be less expensive for him to have? Show work.

(d) For what number of texts, sent and received, would the plans cost the same per month? Show work.

1 B

(a) State the zero(s) of the function. ________

(b) Which of the following is true? 2. ______

      A.   f is an even function.

      B.   f is an odd function.

      C.   f is both even and odd.

      D.   f is neither even nor odd.

Explanation / Answer

1.A) (a) The linear function, that represents Company A's total charge per month for x amount of texts, is :

f(x) = 40+(0.20)*x

(b) The linear function, that represents Company B's total charge per month, is :

g(x) = 60

(c) Putting x = 120 in both functions we get,

f(120) = 40+(0.20)*120 = 40+24 = 64

g(120) = 60

Therefore, Company B's plan will be less expensive for Mark.

(d) Let, for m texts, sent and received, both the plans will cost the same per month.

Then, f(m) = g(m)

i.e., 40+(0.20)*m = 60

i.e., (0.20)*m = 60-40

i.e., (0.20)*m = 20

i.e., m = 20/(0.20)

i.e., m = 100

Therefore, the number of texts will be 100.

1.B) Given, f(x) = x2-9

(a) The zeros of the function at x = -3 and x = 3.

(b) The given function is an even function.

Since, f(-x) = (-x)2-9 = x2-9 = f(x) ,i.e., f(-x) = f(x).

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