**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.

Function Questions Answered

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

Linear Functions

Mr. Barber

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