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4.3 Graph Linear Functions
FUNCTION NOTATION: f(x) = mx + b is the same as y = mx + b.
The symbol f(x) is another name for y and is read “the value of f at x” or “f of x”. Other letters can
be used for f, such as g or h, to name the function.
Ex 1) What is the value of the function f(x) = 2x + 3 when x = –2.
f(x) = 2x + 3
FAMILY OF FUNCTIONS: A group of functions with similar characteristics.
* Functions in the form f(x) = mx + b constitute the family of ____________ functions.
PARENT LINEAR FUNCTION: The most basic function of all linear equations (blue).
f(x) = x is the same as y = x
Graph the function given. Compare it with the graph of the parent function, f(x) = x.
(You will first graph the parent function, so your graph will have two lines.)
g(x) = x – 5
p(x) = x + 2
orange
Same slope as parent
Parallel to parent
Shifted down 5 units from parent
green
Same slope as parent
Parallel to parent
Shifted up 2 units from parent
Graph the function given. Compare it with the graph of the parent function, f(x) = x.
(You will first graph the parent function, so your graph will have two lines.)
h(x) = 2x
purple
Slope is larger than parent, so line is steeper
Same y-intercept as parent, no shift up or down
1
x
3
yellow
Slope is smaller than parent, line is flatter
Same y-intercept as parent, no shift up or down
j(x) =
q(x) = –3x
red
Slope is negative (decreasing), but line is steeper
than the parent because the |-3| = 3
Same y-intercept as parent, no shift up or down
MOVIE TICKETS. The average price of a movie ticket from 1980 to 2000 can be modeled by
the function f(x) = 0.50x + 3 where x is the number of years since 1980.
a. Graph the function.
*must make a t-table.
x
13
y
Cost ($)
0
b. Identify the problem domain and range.
Year 1980-2000 (count by 2’s)
Domain – x values
Your x-values are represented with the number of years since 1980.
D:
Range – y-values
Your y-values are represented with the price ($).
R:
c. Find the value of x so that f(x) = 10.50. Explain what the solution means in this solution.
*set the equation equal to 10.50 and solve for x.
f(x) = 10.50
f(x) = 0.50x + 3