Linear Functions Practice

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1.3 – Linear Functions
Most useful form for
quick graphing
The most basic polynomial function, its points form a line.
Slope intercept form:
y = mx + b
where m = slope
b = y-intercept
Function notation form:
f(x) = ax + b
Graphing calculator use this form
Slope is a very
Standard form:
Ax + By + C = 0
Useful to graph by intercepts
important concept in
that it gives the rate
at which a function
Point slope form:
m (x – x
) = (y – y
)
with point (x
, y
)
a
a
a
a
Δ
changes
y
y
y
rise
=
=
slope =
2
1
m
Slope formula:
better known as
Δ
x
x
x
run
2
1
Rate of change tells one how the function increases or decreases with respect to x. Basically, it is
just a real life way to think about slope.
Ex.
If paid at a rate of 8 dollars an hour then function increase by 8 for every x
Pay = 8 x (hours)
or pay as a function of hours
p(h) = 8h
Ex.
A hot air balloon descends from 1000m at a rate of 50m every 4 seconds.
Height = 1000 – 50/4 (seconds) or
h(t) = -12.5t + 1000
What does this mean as
Ex.
A car travels at a rate of 100km/h
a function? How is
Distance as a function of time
d(t) = 100t
slope related to the rate
of change?
Example 1:
Use slope intercept technique to graph the following linear relations;
a) y = -2x + 5
b) f(x) = ½ x - 2
y-intercept of +5
y-intercept of -2
Start at this point
Start at this point
Slope of -2 (down 2
Slope of ½ (up 1
over +1 pattern)
over +2 pattern)
Example 2:
Use transformations to graph the following linear relations;
Translate key linear
a) g(x) = -2x + 5
b) f(x) = ½ x - 2
point (0,0)
Stretch pattern is 1
over 1 up
Translate y = x
Translate y = x
vertically by +5
vertically by -2
Stretch y = x
Stretch y = x
vertically by -2
vertically by ½
1.3 – linear functions

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