Algebra 2 – Unit 1 Linear Functions and Inequalities
Name:_______________________________________ Period: ______
Unit 1a Review PreAP
Problems 1-3. Sketch the following lines. (Lesson 1.2)
1. A line with a negative slope
(m) and a y-intercept (b) of 0.
2. A line with a slope (m) of 0
and a positive y-intercept (b).
3. A line with a positive slope
(m) and a negative y-intercept (b).
4. To graph the inverse of a relation or function, we reflect it over the parent linear function. What is the
equation of the parent linear function? (Lesson 1.4)
5. Graph the inverse of the line f ( x)  
2
x  3 on
5
the graph to the right.
Add the line y=x (Lesson 1.4)
6. Use the graph on the right to find the equation
of the inverse of the line. (Lesson 1.4)
f(x)
7. Given the function f ( x)  3 x  15 , find the inverse function algebraically. (Lesson 1.4)
What is the slope of this inverse function? m = ___________
Algebra 2 – Unit 1 Linear Functions and Inequalities
8. If f ( x)  3x  4 and g ( x)  2 x  5 , find f ( g ( x)) algebraically. Show your work. (Lesson 1.6)
9. If f ( x)  3x  4 and g ( x)  2 x  5 , find f (g(-3)) algebraically. Show your work. (Lesson 1.5)
Write the domain and range of the given graphs. Use Interval Notation, Inequality Notation, and
Set Notation. (Lesson 1.1)
10.
y
8
6
DOMAIN
RANGE
DOMAIN
RANGE
4
2
x
-8
-6
-4
-2
2
4
6
Inequality Notation
8
-2
Interval Notation
-4
-6
Set Notation
-8
11.
8
6
4
Inequality Notation
2
-8
-6
-4
-2
2
-2
4
6
8
Interval Notation
-4
-6
-8
Set Notation
Algebra 2 – Unit 1 Linear Functions and Inequalities
12. Blood pressure tends to increase with age. Suppose the normal blood pressure of a 20 year old is
120 and that of a 50 year old is 135. Write the equation of the line. (Lesson 1.3)
a. What are the independent and dependent variables?
b. Identify two points on the line that represents this situation.
c. Identify the slope. What does it represent in this situation?
d. Write the equation of the line.
e. Identify the yintercept. What does it represent in this situation?
f. What is the blood pressure of a 30 year old?
g. How old is a person with blood pressure of 140?
13. As scuba divers descend, the pressure of the water increases. Scuba divers can determine their
depth by the pressure. Pressure can be expressed in atmospheres. An atmosphere is equivalent
to 14.7psi (pounds per square inch) of pressure. The table below shows the relationship between
atmospheres of pressure and ocean depth. (Lesson 1.3)
Depth of Ocean (feet)
0 33 66 99 132
Pressure (atmosphere) 1 2
3
4
5
a) Write the equation for the line of best fit for this scenario?
b) If a diver is experiencing 7 atmospheres of pressure, about what depth would he be at?
Algebra 2 – Unit 1 Linear Functions and Inequalities
Are the following functions inverses? (YES/ NO) Prove Algebraically. Show your work.
14. f(x) =
5
𝑥
6
−5
15. f(x) =
2
𝑥
3
+8
6
g(x) = − 5 𝑥 + 6
and
and
g(x) =
3
𝑥
2
− 12
16. Find the domain, range, and end behavior of the following functions.
14
12
DOMAIN
10
8
Inequality Notation
6
4
Interval Notation
2
-5
-4
-3
-2
0
-1-2 0
1
2
3
4
5
Set Notation
-4
-6
End Behavior
RANGE
Algebra 2 – Unit 1 Linear Functions and Inequalities
Use the following functions for Questions 17 and 18:
f(x) = x+4, g(x) = 3x – 1, and h(x) = 6x
17. Find the composite function h( g( f(x))).
18. What is h(g(f(-1)))? ________________
19. For the following questions use the graph below :
10
9
8
7
6
5
4
3
2
1
0
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1-1 0
-2
-3
-4
-5
-6
-7
-8
-9
-10
1
2
3
4
5
6
7
8
9 10
Using Set Notation and the nearest integer:
On what interval is the function decreasing? _______________________________
On what intervals is the function increasing?________________________________
What is the approximate maximum value of this function and when does this occur?
What is the minimum value of this function and when does this occur?
What is the function’s average rate of change on the interval {X| -4<x<-2 }
What is the function’s average rate of change on the interval {X| -1 <x < 1}