Warm Up

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Warm Up
Problem of the Day
Lesson Presentation
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Warm Up Determine if each relationship represents
a function. 1. 2. y 3x2 1 3. For the
function f(x) x2 2, find f(0), f(3), and
f(2).
yes
yes
2, 11, 6
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Problem of the Day Take the first 20 terms of
the geometric sequence 1, 2, 4, 8, 16, 32, . . .
.Why cant you put those 20 numbers into two
groups such that each group has the same sum?
All the numbers except 1 are even, so the sum of
the 20 numbers is odd and cannot be divided into
two equal integer sums.
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Learn to identify linear functions.
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Vocabulary
linear function function notation
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A linear function can be described by a linear
equation. You can use function notation to show
that the output value of the function f, written
f(x), corresponds to the input value x.
The graph of a linear function is a line. The
linear function f(x) mx b has a slope of m and
a y-intercept of b.
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Additional Example 1 Identifying Linear Functions
Determine whether the function f(x) 2x3 is
linear.
f(x) 2x3
Graph the function.
f(x) 2x3 does not represent a linear function
because its graph is not in a straight line.
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Check It Out Example 1
Determine whether the function f(x) -2x 4 is
linear.
f(x) 2x 4
Graph the function.
f(x) -2x 4 does represent a linear function
because its graph is in a straight line. It has a
slope of -2 and a y-intercept of 4.
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Additional Example 2A Writing the Equation for a
Linear Function
Write a rule for the linear function.
Step 1 Identify the y-intercept b from the graph.
b 2
Step 2 Locate another point on the graph, such as
(1, 4).
Step 3 Substitute the x- and y-values of the
point into the equation, f(x) mx b, and solve
for m.
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Additional Example 2A Continued
f(x) mx b
4 m(1) 2 (x, y) (1, 4)
4 m 2
2 2
2 m
The rule is f(x) 2x 2.
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Additional Example 2B Writing the Equation for a
Linear Function
Write a rule for the linear function.
Step 1 Locate two points.
x y
3 8
1 2
1 4
3 10
(1, 4) and (3, 10)
Step 2 Find the slope m.
Step 3 Substitute the x- and y-values of the
point into the equation, f(x) mx b, and solve
for b.
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Additional Example 2B Continued
f(x) mx b
4 3(1) b (x, y) (1, 4)
4 3 b
3 3
1 b
The rule is f(x) 3x 1.
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Check It Out Example 2A
Write a rule for the linear function.
Step 1 Identify the y-intercept b from the graph.
b 1
Step 2 Locate another point on the graph, such as
(5, 2).
Step 3 Substitute the x- and y-values of the
point into the equation, f(x) mx b, and solve
for m.
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Check It Out Example 2A Continued
f(x) mx b
2 m(5) 1 (x, y) (5, 2)
2 5m 1
1 1
1 5m
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Check It Out Example 2B
Write a rule for the linear function.
Step 1 Locate two points.
x y
0 5
1 6
2 7
1 4
(0, 5) and (1, 6)
Step 2 Find the slope m.
Step 3 Substitute the x- and y-values of the
point into the equation, f(x) mx b, and solve
for b.
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Check It Out Example 2B Continued
f(x) mx b
5 1(0) b (x, y) (0, 5)
5 b
The rule is f(x) x 5.
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Example 3 Money Application
A video club cost 15 to join. Each video that is
rented costs 1.50. Find a rule for the linear
function that describes the total cost of renting
videos as a member of the club, and find the
total cost of renting 12 videos.
f(x) mx 15
The y-intercept is the cost to join, 15.
16.5 m(1) 15
With 1 rental the cost will be 16.50.
16.5 m 15
The rule for the function is f(x) 1.5x 15.
After 12 video rentals, the cost will be f(12)
1.5(12) 15 18 15 33.
15 15
1.5 m
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Check It Out Example 3
A book club has a membership fee of 20. Each
book purchased costs 2. Find a rule for the
linear function that describes the total cost of
buying books as a member of the club, and find
the total cost of buying 10 books.
f(x) mx 20
The y-intercept is the cost to join, 20.
With 1 book purchase the cost will be 22.
22 m(1) 20
22 m 20
The rule for the function is f(x) 2x 20.
After 10 books purchases, the cost will be f(10)
2(10) 20 20 20 40.
20 20
2 m
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Lesson Quiz Part I
Determine whether each function is linear. 1.
f(x) 4x2 2. f(x) 3x 1 Write the rule
for the linear function.
not linear
linear
1 2
f(x) x - 1
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Lesson Quiz Part II
Write the rule for each linear function. 2.
3. Andre sells toys at the craft fair. He pays
60 to rent the booth. Materials for his toys are
4.50 per toy. Find a rule for the linear
function that describes Andre's expenses for the
day. Determine his expenses if he sold 25 toys.
x 3 0 3 5 7
y 10 1 8 14 20
f(x) 3x 1
f(x) 4.50x 60 172.50