F-03 Properties of Functions: Domain and Range Warm-Up · Range refers to: Domain and range can be...

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F-03 Properties of Functions: Domain and Range

Warm-Up

1. True or false: the following relation is a function:

{(−1,2), (3, 5), (4, 2)}

2. True or false: the following relation is a function:

{(0, 0), (0, 7), (-2, 4)}

3. How do you test if a graph is a function?

4. Circle which of the following relations represent a function:

a. b. c.

4. If 𝑓(𝑥) = 2𝑥 − 3, what is 𝑓(−2)?

5. If ℎ(𝑡) = 𝑡2 − 3𝑡 + 5, what is ℎ(4)?

6. Let 𝑔(𝑛) =1

2𝑛 − 8. What is 𝑛 if 𝑔(𝑛) = −14?

Functions have a lot of properties. We will only cover the basics in Algebra 1 (you will cover more in

Algebra 2).

Remember that we have an input for a function (typically 𝑥) and an output (typically 𝑓(𝑥) which is

equivalent to 𝑦). We wrote input and output pairs as coordinate points (𝑥, 𝑓(𝑥)).

One of the most important properties of any function is its domain and range.

Domain refers to:

Range refers to:

Domain and range can be written in multiple ways:

1. Set notation:

2. Inequalities*:

3. Interval notation:

When writing domain and range, make sure you do not repeat values and the numbers are always

listed from lowest to highest.

The following relations are not all functions. To practice, we will begin by categorizing each relation

as a function or not a function.

Then, for each relation, list the domain and the range.

We can look at when to use each version of domain and range for certain relations. Not all ways to

write domain and range are applicable to each problem.

Examples

1. {(0,3) , (2, 9) , (-3, 5) , (0, 2) , (1, 1)} a. Function or not?

b. Domain

c. Range

2. a. Function or not?

b. Domain

c. Range

3. a. Function or not?

b. Domain

c. Range

4. a. Function or not?

b. Domain

c. Range

5. a. Function or not?

b. Domain

c. Range

1

2

3

4

4s

-3

0

1

x -2 -1 0 1

y -3 -1 1 3

6. a. Function or not?

b. Domain

c. Range

7. a. Function or not?

b. Domain

c. Range

8. a. Function or not?

b. Domain

c. Range

We can also evaluate functions given portions of their domain. The reason we are able to do this is

because domain is the possible ___________ values, so we can input them into the function.

The range is the possible ___________ values, which we get after inputting the domain.

9. Let 𝑓(𝑥) = 2𝑥 − 7. The domain of the function is {−2, 0, 6}. Find the range.

10. Let 𝑔(𝑥) = 𝑥2 − 3𝑥 + 20. The domain of the function is {−3, 0, 2}. Find the range.