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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
• 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
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}.
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}
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.
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.
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.
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.
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.
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.
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