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# Linear Functions

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by

## Jeemy Barber

on 19 August 2015

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#### Transcript of Linear Functions

Parent Function: f(x) = x
Is it a function? Yes, passes VLT!
Vertical Shifts f(x) = x + b
The Y-Intercept
Adding/Subtracting shifts the graph up or down.
Vertical & Horizontal Stretches
f(x) = mx "The Slope"
multiplying x by m stretches the graph.
Reflection f(x) = -mx
When m is negative, reflects/flips graph over x-axis.
Linear Function f(x) = mx + b
m, stretches vertical/horizontal and reflects (slope)
b shifts up or down (y-intercept)
Writing Equation
Given a y-intercept of 5, and a slope of 2/3, write a linear equation.
Yes, it is a function
Domain/Range: All Real #'s
Always decreasing ( m is negative)
As x increases, y decreases
Thanks For Listening
Group Members: Mr. Barber
NOW IT'S YOUR TURN!
Family of Functions
Linear Functions

Mr. Barber

X and Y intercept are at (0,0)
As x increases, y increases
As x decreases, y decreases
Domain/Range: All Real #'s
Characteristics
X and Y always the same
Always increasing
f(x) = x + 5
f(x) = x - 4
Changes table by adding
or subtracting b value
from x.
f(x) = x + 12, would
shift graph up 12 units
f(x) = x - 3, would shift
graph down 3 units.
|m| > 1, stretches
vertically.
0 < |m| < 1, stretches
horizontally.
f(x) = 3x
f(x) = 0.5x
vertical stretches cause y to increase quickly
horizontal stretches cause y to increase slowly.
f(x) = x
f(x) = -x
as x increases
y decreases
X values changes
in table
f(x) = -4x + 3
f(x) = -4x + 3
reflects over x-axis
stretches vertically
by a multiplier of 4
shifts up 3
slope is -4, y-int is (0,3)
f(x) = 2/3x + 5
Given f(x) = -0.5x, find the slope and y-intercept.
slope = -0.5 y-intercept is 0
f(x) = -4x + 3
As x decreases, y increases
x-int (.75,0)
y-int (0,3)
Inverse is a function
No critical points.
Graphs made at www.desmos.com
Full transcript