College Algebra
MATH 140 Unit 1 Review
The test for Unit 1 covers material from sections 2.5,3.1-3.5,6.1,6.2 of your text, Algebra and Trigonometry 8 th Ed. by Sullivan. You are responsible for the topics covered in these sections. Be sure that you review the homework and can do the problems assigned. Go over the quizzes, too.
In particular, be sure that you can do the following:
1.
Given an equation in and , decide if is a function of .
Example
Is a function of if ?
2.
Given an algebraic formula for a function, evaluate the function for specified input values.
Example
Let . Find the value for , , and .
3.
Given the algebraic formula for a function, find the domain of the function.
Example
Find the domain for the function given by .
4.
Given the graph for a function, find the domain and the range.

Example
Give the domain and range for the function whose graph is given below.
5.
Given a graph in the
,
plane, use the vertical line test to determine if is a function of .
Example
Decide if the following graph gives as a function of . Explain your answer.

6.
Given the graph for a function, determine the intervals over which a function is increasing, decreasing, or constant.
Example
Consider the graph of the function shown below. Is the function ever decreasing? If so, give the interval on over which this behavior occurs.
7.
Given the graph for a function, determine if the function is even, odd, or neither.
Example
Consider the graph of the function shown immediately above. Is the function even, odd, or neither? Explain how you decide.
8.
Given the graph for a function, determine if the function is one-to-one.
Example
Consider the graph of the function shown immediately above. Is the function one-to-one? Explain how you decide.
9.
Given the algebraic formula(s) for a function, construct the graph for the function.
Example
Graph the function:

10.
Given and algebraically, find the formula and give the domain for the sum, difference, product and quotient of the functions.
Example
, , , and Let and . Find the formulas for
State any restrictions on the domain for these functions.
11.
Given and algebraically, find the formulas for the composite functions.
Example
.
Let and . Find the formulas for and .
12.
Given the algebraic formula for a function, find the formula for the inverse function and check your answer.
Example
Let . Find and check your work.
13.
Construct and use mathematical models for variation.
Examples a) Write the mathematical model for the statement “ varies inversely with and directly with ” using as the constant of proportionality.
b) Write the mathematical model for the statement “ is inversely proportional to ” given that
when . Then use your model to find the value of when .