Piecewise Function

Question

Using the piecewise function P(x)={3x-45, 0 ≤ x ≤ 50}, {3x-65, 50 < x ≤ 100}, {3x-85, 100 < x ≤ 150}

Find P(10) and P(50) and explain why they satisfy the first part of the function which is 3x-45, 0 ≤ x ≤ 50.

Answer 1

So I'm guessing you've already found P(10) = -15 and P(50) = 105. Otherwise, this is simply a location question. Since the values are in the range (0, 50], their P(x) values will be using the first part. x=50 is not included in the second part of the function, so we wouldn't use that part to find P(50).

Answer 2

Both values meet the conditions for the first equation.

P(10)=3(10)-45 = -15

P(50)=3(50)-45 = 105

0 ≤ 10 ≤ 50 and 0 ≤ 50 ≤ 50 is the reason the first equation is used for both.

Answer 3

Because 3x-45 is valid on [0,50], P(10) = 3(10)-45 = -15 and P(50) = 3(50)-45 = 105. Note that [0,50] is a result of the fact that 0≤x≤50. Hope that helps!