1.7 Warm Up
1. Find the slope and y-intercept:
a. y = 2x – 5 b. 9x + y = 8
c. 8y – 2x = 4
2. Graph the equation:
a. y = -2/3 x + 1
b. y = 4/3 x - 5
1.7 Graphing Linear
Functions
Vocabulary
• Function notation: f(x) read f of x
– Linear function notation: f(x) = mx + b
– It is the same as saying “y”
• Family of functions: have same
characteristics
• Parent linear function: most basic
f(x) = x
EXAMPLE 1
Standardized Test Practice
EXAMPLE 2
Find an x-value
For the function f(x) = 2x – 10, find the value of x so that
f(x) = 6.
EXAMPLE 4 Compare graphs with the graph f (x) = x
Graph the function. Compare the graph with the graph
of f (x) = x.
a.
g(x) = x + 3
SOLUTION
Because the graphs of g and
f have the same slope, m = 1,
the lines are parallel. Also,
the y- intercept of the graph
of g is 3 more than the yintercept of the graph of f.
EXAMPLE 4 Compare graphs with the graph f (x) = x
b.
h(x) = 2x
SOLUTION
The graph is a vertical
stretch of the parent
function by a scale factor
of 2.
Write an equation
from4 a graph
for Example
GUIDED PRACTICE
3. Graph h(x) = – 3x. Compare the graph with the
graph of f (x) = x.
SOLUTION
The graph is a vertical
stretch of the parent
function by a scale factor
of 3 and a reflection over
the x-axis.
•
Compare the functions to the graph of
f(x) = x.
a. f(x) = 5x
b. f(x) = -1/2 x
c. f(x) = x – 2
d. f(x) = x + 8
Matching
•
Match the function w/ its description in
relation to the graph of f(x)=x.
1. g(x) = 4x 2. g(x) = x + 4
3. g(x) = x – 4
a. Vertical shift of 4 units up
b. Vertical shift of 4 units down
c. Vertical stretch w/ a scale factor of 4
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y = -2x – 1
y = 1/3 x + 1
y = 4/3 x – 4
y = -3x
y = -2x + 5
y = 1/7 x – 3
y = 9x
y = -8x + 3
y = 1/5 x + 3
y = -1/2 x - 2
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y=½x–9
y = -1/6 x
y = -4x – 4
y = -1/5 x – 8
y = 6x + 6
y = 5x – 2
y = -3x + 2
y = -1/9 x – 2
y = 8/7x + 4