1.6 part IParent Functions

Library of FunctionsYou should be familiar with the shapes of these basic functions.

1.6 Parent Functions

• The constant function, f(x) = c• The linear function, f(x) = x• The absolute value function, f(x) = |x|• The square root function, f(x) = √x• The quadratic function, f(x) = x2

• The cubic function, , f(x) = x3

• The reciprocal function, f(x) = 1/x• The greatest integer function, f(x) = [|x|]

PARENT FUNCTIONS

Write a linear function given f(2) = 4 and f(5) =−1.

m = −1 − 4 5 − 2

m = − 5 3

First find the slope and then use point-slope form.

y – y1 = m(x – x1)

y – y1 = m(x – x1) 4 2

GRAPH

GIVEN: f(2) = 4 AND f(5) =−1

HOW DID THE GRAPHS SHIFT?

HOW DID THE GRAPHS SHIFT?

Write an equation for each shift

1. Parent function:|x| left 4, down 7 f(x) = |x+4|-7

2. Parent function: right 1, up 5

3. Parent function: refects across x-axis, right 2