vocabulary independent variable dependent variable vertical line test function notation
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• independent variable
• dependent variable
• vertical line test
• function notation
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Relation: a set of ordered pairs
Domain: the set of x values of the relationRange: the set of y values of the relation
Function: a relation in which each member of of the domain is paired with one and only one member of the range
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Methods of testing for a function:
Inspect the ordered pairs. If each x is different it is a function. If 2 x values are thesame, it is not a function.
Vertical line test: Look at the graph of therelation. If every point is on a separate vertical line, it is a function. If 2 or morepoints are on the same vertical line, it is nota function.
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Determine Whether a Relation is a Function
A. Determine whether the relation is a function. Explain.
(3, 48), (7, 21), (5, 15), (1, 13), (2, 12)
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Determine Whether a Relation is a Function
B. Determine whether the relation is a function. Explain.
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A. A
B. B
C. C
D. D
A. Determine whether the relation is a function. Explain. {(1, 5), (–2, 7), (3, 8), (4, 5)}
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A. A
B. B
C. C
D. D
B. Determine whether the relation is a function. Explain.
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Use a Graph to Identify Functions
Determine whether the graph is a function. Explain your answer.
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A. A
B. B
C. C
D. D
Determine whether the graph is a function. Explain.
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Function Notation: f(x) =
Examples: f(x) = 2x + 3
g(x) = x2
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Find a Function Value
A. If f(x) = 6x + 5, what is the function value of f(5)?
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Find a Function Value
B. If f(x) = 6x + 5, what is the function value of f(–4)?
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A. A
B. B
C. C
D. D
A. If f(x) = 2x – 7, what is the value of f(4)?
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A. A
B. B
C. C
D. D
B. If f(x) = 2x – 7, what is the value of f(–3)?
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Use Function Notation
A. GREETING CARDS Ms. Newman spent $8.82 buying cards that sold for $0.49 each. Use function notation to write an equation that gives the total cost as a function of the number of cards purchased.
Answer: t(c) = 0.49c
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Use Function Notation
B. GREETING CARDS Ms. Newman spent $8.82 buying cards that sold for $0.49 each. Use the equation to determine the number of cards purchased.
t(c) = 0.49c Write the function.
8.82 = 0.49c Replace t(c) with 8.82.
18 = c Divide each side by 0.49.
Answer: So, Mrs. Newman bought 18 cards.
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A. A
B. B
C. C
D. D
A. CANDY BARS Erik bought candy bars that cost $0.59 cents each. Which function describes his purchase if t(c) = total cost and c = the number of candy bars?
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A. A
B. B
C. C
D. D
B. CANDY BARS Erik bought candy bars that cost $0.59 cents each and spent $4.72. If t(c) = total cost and c = the number of candy bars, use the function t(c) = 0.59c to find the number of candy bars purchased.