Main Idea and New VocabularyExample 1:Find a Function ValueExample 2:Make a Function TableExample 3:Real-World Example: Independent and Dependent VariablesExample 4:Real-World Example: Analyze Domain and RangeExample 5: Real-World Example: Write and

Evaluate a Function

• Complete function tables.

• function• function table• independent variable• dependent variable

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) = –18 + 4 or –14 Simplify.

Answer: So, f(–6) = –14.

Find f(–2) if f(x) = 4x + 5.

A. –13

B. –3

C. 3

D. 13

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.

Make a Function Table

Answer: The domain is {–2, –1, 0, 1}. The range is{–9, –5, –1, 3}.

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}

C. domain: {–2, –1, 0, 1}range: {1, 3, 5}

D. domain: {–1, 1, 3, 5} range: {–2, –1, 0, 1}

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.

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.

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.

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.

Analyze Domain and Range

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 CYP

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.

A. 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 275. The range will be whole numbers.

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.

Write and Evaluate a Function

The function c(ℓ) = 8ℓ + 75 represents the situation.

To find the cost for 13 lessons, substitute 13 for ℓ.

Answer: It will cost $179 for 13 lessons.

Write and Evaluate a Function

c(ℓ) = 8ℓ + 75 Write the function.

c(ℓ) = 8(13) + 75 or 179 Substitute 13 for ℓ.

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