2. Main Idea and New Vocabulary Example 1: Find a Function Value
Example 2: Make a Function Table
Example 3: Real-World Example: Independent and Dependent Variables
Example 4: Real-World Example: Analyze Domain and Range
Example 5: Real-World Example: Write and Evaluate a Function
Lesson Menu

3. Complete function tables.
independent variable
dependent variable
Main Idea/Vocabulary

4. f(x) = 3x + 4 Write the function.
Find a Function Value
Find f(–6) if f(x) = 3x + 4.
f(x) = 3x + 4 Write the function.
f(–6) = 3(–6) + 4 Substitute –6 for x into the function rule.
f(–6) = – or –14 Simplify.
Answer: So, f(–6) = –14.
Example 1

5. Find f(–2) if f(x) = 4x + 5.
A. –13
B. –3
C. 3
D. 13
Example 1 CYP

6. Make a Function Table
Choose four values for x to make a function table for f(x) = 4x – 1. Then state the domain and range of the function.
Substitute each domain value x into the function rule. Then simplify to find the range value.
Answer: The domain is {–2, –1, 0, 1}. The range is {–9, –5, –1, 3}.
Example 2

7. A. domain: {−2, −1, 1} range: {0, 1, 3, 5}
Use the values –2, –1, 0, 1 for x to make a function table for f(x) = 2x + 3. State the domain and range of the function.
A. domain: {−2, −1, 1} range: {0, 1, 3, 5}
B. domain: {–2, –1, 0, 1} range: {–1, 1, 3, 5}
domain: {–2, –1, 0, 1} range: {1, 3, 5}
D. domain: {–1, 1, 3, 5} range: {–2, –1, 0, 1}
Example 2 CYP

8. Independent and Dependent Variables
FOOD Linda buys a can of tuna fish that weighs 4.2 ounces. The total weight w of any number of cans c of tuna fish can be represented by the function w(c) = 4.2c. Identify the independent and dependent variables.
Answer: Since the total weight of the cans depends on the number of cans, the total weight w is the dependent variable and the number of cans c is the independent variable.
Example 3

9. FOOD There are approximately 275 miniature marshmallows in a 10
FOOD There are approximately 275 miniature marshmallows in a 10.5-ounce bag of marshmallows. The total number of marshmallows m in any number of bags b can be represented by the function m(b) = 275b. Identify the independent and dependent variables.
A. The number of marshmallows m is the dependent variable. The number of bags b is the independent variable.
B. The number of bags b is the dependent variable. The number of marshmallows m is the independent variable.
Example 3 CYP

10. Analyze Domain and Range
FOOD Linda buys a can of tuna fish that weighs 4.2 ounces. The total weight w of any number of cans c of tuna fish can be represented by the function w(c) = 4.2c. What values of the domain and range make sense for this situation? Explain.
Answer: Only whole numbers make sense for the domain because you cannot buy a fraction of a can of tuna fish. The range values depend on the domain values, so the range will be rational number multiples of 4.2.
Example 4

11. FOOD There are approximately 275 miniature marshmallows in a 10
FOOD There are approximately 275 miniature marshmallows in a 10.5-ounce bag of marshmallows. The total number of marshmallows m in any number of bags b can be represented by the function m(b) = 275b. What values of the domain and range make sense for this situation? Explain.
Only positive rational numbers make sense for the domain. The range will be multiples of 275.
B. Only whole numbers make sense for the domain. The range will be multiples of 10.5.
C. Only whole numbers make sense for the domain. The range will be multiples of 275.
D. The domain will be multiples of The range will be whole numbers.
Example 4 CYP

12. Write and Evaluate a Function
DANCE A dance studio charges an initial fee of $75 plus $8 per lesson. Write a function to represent the cost c(ℓ) for ℓ lessons. Then determine the cost for 13 lessons.
The function c(ℓ) = 8ℓ + 75 represents the situation.
Example 5

13. Write and Evaluate a Function
To find the cost for 13 lessons, substitute 13 for ℓ.
c(ℓ) = 8ℓ + 75 Write the function.
c(ℓ) = 8(13) + 75 or 179 Substitute 13 for ℓ.
Answer: It will cost $179 for 13 lessons.
Example 5

14. PHOTOGRAPHY A photographer charges a $55 sitting fee plus $15 for each pose. Write a function to represent the cost c(p) for p poses. Then determine the cost for 8 poses.
A. c(p) = 55c + 15; $455
B. c(p) = 15c + 55; $175
C. c(p) = 55p + 15; $455
D. c(p) = 15p + 55; $175
Example 5 CYP