Parent FunctionsGeneral Forms

Transforming linear and quadratic function

Linear FunctionO Has a momma equation: y=xO This graph can shift up, down, right,

left, or get steeper or flatter

Linear FunctionO f(x)=x

X intercept:

Y intercept:

Slope:

Linear FunctionO f(x)=xO Domain: all real numbersO Range: all real numbers

TransformationsLinear and Quadratic

Vertical ShiftsO The y intercept changesO F(x) changes to f(x)=x+kO If k is greater than 0 the intercept

moves up k unitsO If k is less than 0, the intercept

moves down k unitsO http://merganser.math.gvsu.edu/m2

21/transform/linear.html

Horizontal ShiftO The input value changesO F(x) changes to f(x+h) O Wherever there was an x in the

equation it is now replaced with x+h

Horizontal ShiftsO If h is greater than 0, shift is to the

leftO If h is less than 0, shift is to the rightO Opposite of what you would think

Reflection across y axisO The input value changesO F(x) changes to f(-x)O Lines are symmetric about the y axis

Reflection across the x axis

O The slope of the line changes signsO F(x) changes to –f(x)O Looks exactly like a reflection across

the y axis for a linear function

Changing the steepness

O The number in front of the x is larger than 1- slope is larger, line is steeper

O The number in front of the x is smaller than 1- the slope is smaller, the line is flatter

ExampleO Describe the change in the original

equationO F(x)=2x+3O Momma equation was:O We have now….O TI Smart View

Checking on the Calculator

O In y1 put xO In y2 put the new functionO Look at the difference

Try AnotherO Sketch the new graph/Describe the

changesO F(x)=3(x+1)+4

AnotherO Write the equation describing the

shiftO The momma equation is f(x)=x.

There is a vertical shift down by 2 and the slope is increased by 5

AnotherO How would I change the previous

problem to include a shift to the left of 2?