Name: ______
Based on the results of your chapter 4 indicator, the following skills and concepts need to be remediated in preparation for your chapter assessment.
Skills / Worksheets to be completedInterpreting Graphs
Functions vs. Relations
Evaluating Functions
Composition of Functions
Domain and Range
Inverse Functions
This will be put in as a formative assessment grade.
Functions vs. Relations
Determine whether each relation is a function or not. Explain your reasoning for each.
1. {(3,2), (1, -1), (2, -4), (3, -9), (4, -16)}
2.
3. y2 = x
X / 2 / 6 / -2 / 14 / 1.5Y / 5 / 7 / 9 / -2 / 7
X / 2 / 6 / -2 / 8 / 6
Y / 5 / 7 / 9 / -2 / 4
Evaluating Functions
Use the following 5 functions, f(x), g(x), m(x), and n(x), to evaluate the problems below.
g(x)
m(x) = 7x – 4 n(x) = (x - 2)2 + 1 p(x) = -3x2 + 2x - 1
------
Evaluate.
1. f(2) 2. x when f(x) = 2 3. g(-3) 4. x when g(x) = 3
5. m(5) 6. x when m(x) = -32 7. n(-2) 8. x when n(x) = 26
9. (m – p)(x) 10. 11. 12. g(11) + m(2)
Domain and Range
State the domain and range of each relation.
1. {(3,2), (1, -1), (2, -4), (3, -9), (4, -16)}
2.
3.
Interpreting Graphs
1. The following graph tells a story about Peter’s walk to school. Answer the following questions about the graph
a. What is the independent and dependent variable?
b. What is the meaning of the y-intercept?
c. What do the increasing parts of the graph mean? What does the decreasing part of the graph mean?
2. Juliet is 5 feet tall. She throws a rock at Romeo’s window which is 15 feet off of the ground. It takes 2 seconds for the rock to hit the window and 2.5 seconds for the rock to fall back to the ground. Draw a graph to represent the time and height of the rock. Remember to label the axes.
3. Describe each of the following key features of the graph of
f(x) = (x + 1)2(x - 1)3(x - 3)
a. Where does the graph intersect the x-axis?
b. Where does the graph intersect the y-axis?
c. Is the graph increasing or decreasing for 0 x 2?
d. Is the value of f positive or negative when x<-2?
Composition of Functions
1. Use the following 5 functions, f(x), g(x), m(x), and n(x), to evaluate the problems below.
g(x)
m(x) = 7x – 4
n(x) = (x - 2)2 + 1
p(x) = -3x2 + 2x - 1
------
a. m(f(1)) b. c. m(f(g(3))) d.
2. Complete the following table.
x / -1 / 2 / 3 / 4f(x) / 3 / -1 / 4 / 2
g(x) / 2 / 3 / -1 / 4
f(g(x)) / f(g(-1))=
g(f(x)) / g(f(3))=
Inverse Functions
1. Sketch the inverse of the graph. Is the new graph a function?
2. Determine the inverse of the functions.
a. f(x) = 2x – 5 b. c.
d. h(x) = e. g(x) =
3. Prove that the functions are inverses of each other.
a. f-1(x) = 3x + 12 and f(x) = b. f-1(x) = and f(x) = 5x+7
Answers
Interpreting graphs
1. a. Independent: Time; Dependent: Distance from home b. Starting from home
c. Increasing – Farther away from home; Decreasing – closer to home
2.
3. a. x = -1, 1, 3 b. y = 3
c. decreasing d. positive
3
Functions vs. Relations
1. No (3, 2) and (3, -9) 2. Yes, passes the vertical line test
3. No, example: if x = 25, then y = 5 or -5
4. Yes, all the x’s are different
5. No, (6,7) and (6,4)
Evaluating Functions
1. -4 2. 3 3. 8 4. 0, 5, and 9 5. 31 6. -4
7. 17 8. 7 and -3 9. 3x2 + 5x – 3 10. -21x3 + 26x2 – 15x + 4
11. -1 12. 5
Composition of Functions
1. a. -11 b. 1.25 c. -32 d. -21t2 + 14t – 7
2. f(g(x)) = -1, 4, 3, 2; g(f(x)) = -1, 2, 4, 3
Domain and Range
1. Domain: {3, 1, 2, 4} Range: {2, -1, -4, -9, -16} 2. Domain: -3 x 11 Range: -5 y < 9
3. Domain: {-2, 1, 3, 4.5} Range: P{1, 2, 3, 4, 5}
Inverse Functions
1. yes 2. a. b. c.
d. e.
2. a. f-1() = x f(3x + 12) = x
b. f-1(5x+7) = x f() = x