Shifting Functions

Module 3 Lesson 4

Radical standard form

‘a’ describes the vertical shrink or stretch. If it is 1, then there is no stretch. If a is between 0 and 1 (0<a<1) then it is a shrink by that much. If a>1 then it is a stretch by that much. If a is negative then the function reflects across the x-axis.

‘h’ is the horizontal shift left or right

‘k’ is the vertical shift up or down

Parent Function

▪ We can the original function with no shifts the parent function. The equation is

▪ Here is a picture of the graph:

What do the shifts look like?

, right two , right two down 4

Referring to the rules and the last 2 examples, do you know the equation of the graph below?

Answer below

▪ Since the graph goes to the left three you have x- -3, which makes x+3.

▪ Since it goes down 6, you have a -6 after the radical.

▪ Answer:

What about stretches and shrinks?

vertical stretch by 3 vertical shrink by 1/3