Math 141 – Online Take Home Set #2
Due: Tuesday – April 25, 2017
Name: _______________________________
Spring 2017
Max Points: _______ / 40
Directions: Place work in the space provided. If you need more room attach work on a separate sheet of
paper. I expect a well-organized and easy to read solution set. Be sure to place enough detail, so as the
reader does not have to make any assumptions to your work. You are more than welcome to ask me
questions, but other than that work alone. Happy problem solving and “May the Force Be With You.”
Problem 1: [4 points] Use the values given in the table
x
y
1
8
2
14
2.8
17
to find the average rate of change on the following intervals:
(a) [1, 4]
(b) [2.8, 5.3]
Problem 2: [6 points] Let 𝑓(𝑥) = 4𝑥 − 𝑥 2 , find the average rate of change from:
(a) x = -1 to x = 3
(b) x = 1 to x = 5
(c) What is the equation of the secant line connecting the points (1, f(1)) and (5, f(5)).
3.1
21
4
25
5.3
29
Problem 3 [6 points] Suppose an object is thrown upward with an initial velocity of 52 feet per second from
a height of 125 feet. The height, in feet, of the object t seconds after it is thrown is given by the function
ℎ(𝑡) = −16𝑡 2 + 52𝑡 + 125.
(a) Find the average velocity in the first three seconds after the object is thrown. (don’t forget units)
(b) Find the average velocity when the object is between 2 seconds and 4 seconds. (don’t forget units)
Problem 3: [6 points] If the points (-4, 6) and (2,-2) are on the graph of the function 𝑦 = 𝑓( 𝑥) then
(a) State the points that are on the graph of 𝑔(𝑥) = 𝑓(𝑥 + 3) − 2
(b) State the points that are on the graph of ℎ(𝑥) = −2𝑓(−𝑥)
2
(c) State the points that are on the graph of 𝐾(𝑥) = 𝑓 (3 𝑥)
Problem 4: [4 points] Suppose the graph of some function 𝑦 = 𝑆𝐼𝐶𝐾(𝑢) is given as in each figure. Then
sketch the graph of the appropriate transformed graph.
(a) 𝑚(𝑢) = −𝑆𝐼𝐶𝐾(𝑢)
(b) 𝑝(𝑢) = 𝑆𝐼𝐶𝐾(−𝑢)
y
y
u
Problem 5 [5 points]
u
9 − 𝑥 2 𝑖𝑓
𝑥 < −1
Sketch the piecewise function defined by 𝑀(𝑥) = {√𝑥 + 1
𝑖𝑓 − 1 ≤ 𝑥 < 3
6−𝑥
𝑖𝑓
𝑥≥3
Problem 6: [9 points]
Answer the questions below based on the following graph for 𝑦 = ℎ(𝑥)
(a) Evaluate: ℎ(−3) =
ℎ(5) =
ℎ(8)−ℎ(12)
8−12
=
(b) What is the Domain of the function? What is the Range of the function?
(c) On what interval(s) is ℎ(𝑥) < 0?
(d) On what interval(s) is ℎ(𝑥) decreasing?
(e) Where does the Local Maximum value occur? What is the Local Maximum value?