Lesson 1.2.5
HW: 1-78 to 1-82
Learning Target: Scholars will be able to describe the domain and range of a relation by
examining an equation or graph.
You have many characteristics that you can describe about graphs and functions using the
questions that you began developing in Lesson 1.2.1. You also have learned how to tell if a
relationship is a function. Today you will complete your focus on functions by describing the
inputs and outputs of functions.
1-71. Examine the graph of the relationship below.
Use it to estimate:
1.
2.
3.
4.
y when x = –4
y when x = 1
y when x = 4
Is this relation a function? Why or why not?
1-72. Examine the relation shown below .
1. Find f(−3), f(0), and f(2).
2. Find f(3). What happened?
3. Are there any other inputs that cannot be evaluated by this function? In other words, are
there any other values that x cannot be? Explain how you know.
4. The set (collection) of numbers that can be used for x in a function and still get an
output is called the domain of the function. The domain is a description or list of all the
possible x-values for the function. Describe the domain of
.
5. What other types of functions have you looked at thus far in this course or in previous
courses that have limited domains? How were they limited?
1-73. Now examine g(x) graphed at right.
1.
2.
3.
4.
5.
Is g(x) a function? How can you tell?
Which x-values have points on the graph? That is, what is the domain of g(x)?
What are the possible outputs for g(x)? This is called the range of the function.
Ricky thinks the range of g(x) is: −1, 0, 1, 2, and 3. Is he correct? Why or why not?
What other functions have you worked with previously in this course or previous courses
that have limited ranges? How were they limited?
1-74. FINDING DOMAIN AND RANGE
The domain and range are good descriptors of a function because they help you know what
numbers can go into and come out of a function. The domain and range can also help you set up
useful axes when graphing and help you describe special points on a graph (such as a missing
point or the lowest point).
Work with your team to describe in words the domain and range of each relationship
below. Then state whether or not the relationship is also a function.

1-78. Which of the relationships below are functions? If a relationship is not a function,
give a reason to support your conclusion.
1.
2.
x y
−3 19
5 19
19 0
0 −3
4.
x
y
7 −2 0
10 0 10
7
3
4
0
5.
1-79. Find the x- and y-intercepts for the graphs of the relationships in problem 1-78.
1-80. Find the inputs for the following functions with the given outputs. If there is no
possible input for the given output, explain why not.
6.
7.




1-81. Use the relationship graphed at right to answer the questions below.
1. Is the relation a function?
2. What is the domain?
3. What is the range?
1-82. What value(s) of x will make each equation true?
1.
2.
3.
Lesson 1.2.5

1-71. See below:
1. ≈ –2.3, 0, 3.3
2. 2, –3
3. ≈ –3.7
4. No; some inputs have multiple output values.

1-72. See below:
1. –1, –2, –6
2. There is no solutuion because you cannot divide by zero.
3. No; the error occurs when the denominator is 0, and 3 is the only value that causes that
to happen.
4. All real numbers except x = 3.
5. Possible response: Square root. Values of x that make the expression inside the square
root negative are not allowed.

1-73. See below:
1. Yes; each input has exactly one output.
2. D: –2 ≤ x ≤ 4
3. R: –1 ≤ y ≤ 3
4. No; he is missing all the values between those numbers. The curve is continuous, so our
description needs to include all the numbers, not just the integers.
5. Possible examples include absolute value and parabolas.

1-74. While students will describe these with words, we have provided some solutions using
inequality notation due to space considerations. Parts (b), (c), (d), and (f) are functions. The
others are not. See solutions below.
1. D: –3 ≤ x ≤ 3 R: –3 ≤ y ≤ 3
2. D: all real numbers, R: all real numbers
3. D: –2 ≤ x ≤ 4 R: –4 ≤ x ≤ 2
4. D: all real numbers, R: y ≤ 4
5. D: –2 ≤ x ≤ 4 R: –3 ≤ y ≤ 2
6. D: x ≥ 0, R: y ≥ 3

1-78. See below:
1. Not a function because more than one y-value is assigned for x between –1 and 1
inclusive
2. Appears to be a function
3. Not a function because there are two different y-values for x = 7
4. Function

1-79. See below:
1. x-intercepts (–1, 0) and (1, 0), y-intercepts (0, –1) and (0, 4)
2. x-intercept (19, 0), y-intercept (0, –3)
3. x-intercepts (–2, 0) and (4, 0), y-intercept (0, 10)
4. x-intercepts (–1, 0) and (1, 0), y-intercept (0, –1)

1-80. See below:
1. 2
2. 53

1-81.
1.
2.
3.
See below:
yes
–6 ≤ x ≤ 6
–4 ≤ y ≤ 4

1-82.
1.
2.
3.
See below:
x = –8
x = 144
x = 3 x = −5