Warm Up What is the domain, range, max/min,

interval of increase and decrease for the following graph (list critical points first)

Parent Function Transformation

Lesson Essential Question – How do we move graphs?

f(x) = x

f(x) = x²

f(x) = x³

f(x) = √x

f(x) = lxl

f(x) = 1/x

Putting a NEGATIVE in front What happens when we put a negative

in front of the function?

There is a reflection

Y = - x

See how it flipped? because of the –x

Does it flip over the x or y axis?

Y = -lxl

Reflection over x or y?

Y = -x³

Reflection over x or y?

Y = -x²

Reflection over x or y?

Adding a “+” to it Adding a “+” shifts that whole function

(from the critical point) UP the y axis that many points.

If it is +3, then the graph shifts up 3

Y = x + 6

Start at the origin (0,0) and move up 6

Y = lxl + 2

Always start at the origin

Y = √x + 3

What happens if we have a NEGATIVE?

Then the entire graph moves DOWN the y axis that many points

If you have a “- 4”, then you move down the y axis 4 points from the origin.

Y = x² - 4

Y = x³ - 3

Y = √x – 4

Let’s Review A negative IN FRONT of the x means it

is a reflection

Is this a reflection over the X or Y axis?

Let’s Review A “+” AFTER the x means you move it up

the y axis

Always start at the origin then move

Let’s Review A “-” after the x means you move it

down the y axis

Let’s Confuse Sometimes you will have to do 2 things

Like a reflection AND move it up the y axis

You need to pay attention to the equation to figure out what to do

Y = - lxl + 2

Y = -x + 1

Y = -x² + 1