Algebra 2
1.1 to 1.4 Review
Name: _______________________________________________ Date: __________________________________ Hour: _______
Describe the interval show using an inequality, set notation, and interval notation (Lesson 1.1).
1.
2.
Inequality:
Set Notation:
Interval Notation:
Inequality:
Set Notation:
Interval Notation:
3.
4.
Inequality:
Set Notation:
Interval Notation:
Inequality:
Set Notation:
Interval Notation:
Describe the domain and range of the graph using an inequality, set notation, and interval
notation. Then describe the end behavior (Lesson 1.1).
5.
6.
7.
Draw the graph of the function with its given domain. Then determine the range using interval
notation (Lesson 1.1).
8. f ( x)  2 x  3, Domain : (0,3]
9. g ( x)   x  1, Domain : [4,1)
Range: __________
Range: __________
10. g ( x) 
3
x  4, Domain : [2, )
2
Range: __________
Use the graph to find: intervals where the function is increasing and decreasing, the local
maximum & minimum values, the zeros, the domain & range, and the end behavior. Use
inequalities to describe the intervals. (Lesson 1.2)
11.
12.
(-0.8, 0)
(1.6, 2)
(2.8, 0)
Increasing:
zeros:
Increasing:
zeros:
Decreasing:
Domain:
Decreasing:
Domain:
Local maximum:
Range:
Local maximum:
Range:
Local Minimum:
E.B.:
Local Minimum:
E.B.:
The graph of f(x) is given. Use transformations to graph the related function g(x). Remember
your reference points: (-1, 1), (0, 0) , and (1, 1)
13. g ( x)   f ( x  3)  2
14. g ( x)  2 f ( x  4)  1
16. g ( x)  
15. g ( x)  f (2( x  1))  3
1
f ( x  3)
3
Let g(x) be the transformation of f(x). Write the rule for the function g(x).
17. Translation 8 units right
18. Vertical stretch by a factor 3, translation up 2
19. Reflection across the x-axis, horizontal stretch by a factor of 2, and a translation left 5 units.
1
20. Horizontal compression by a factor of 3, translation right 2 units and down 3 units.
Tell whether each function is one-to-one or many-to-one. Then determine whether the inverse
is a function.
21. Function:
Domain:
Inverse
Range:
1
2
3
4
Domain:
22. Function:
Range:
Domain:
-2
1
6
3
9
5
Inverse
Range:
2
4
6
8
Domain:
Range:
Find the inverse of each function. Then graph it.
23. f ( x)  x  3
24. f ( x)  2 x  4
1
25. f ( x)   x  1
3
4
26. f ( x)   x  1
3
Write an equation for the situation, and identify the domain and range in inequality notation.
(1.1)
27. Jeremy went on a jog and ran one mile every 8 minutes. He ran for 56 minutes. Write an equation
for the distance Jeremy jogged in miles as a function on time in minutes.
Function: ________________________________
Domain: __________________________________
Range: ____________________________________