1. 2. Do Now 3. 4. Describe the transformations. 1. 2. What is the domain and range: 3. 4. Domain: Domain: Range: Range:

Absolute Value Functions

Absolute Value By definition, absolute value is the distance from zero. Can we ever have a negative distance? How far away from zero is 3? How about -2?

Absolute value How many ways are there to be 4 units away from zero?

Evaluating absolute value Evaluating an absolute value expression still requires PEMDAS. We treat absolute value bars like parenthesis, so we want to simplify inside of the bars first. Example: Evaluate when x = 1.

Examples:

Graphing absolute value functions Why do you think the graph looks like this?

Domain and Range Domain: Range:

Graphing absolute value functions This will always give us the basic shape of our absolute value functions. We will use what we know about transformations to shift the graph.

Check this in your calculator. Based on what happened to radicals, describe the transformations that might occur for each of the following from the parent function: Check this in your calculator.

How Absolute Value Functions Move Add/Subtract INSIDE the bars: opposite direction, left and right Multiply by a value greater than 1 in FRONT: stretch (skinny), slope of right side Multiply by a value between 0 and 1 in FRONT: wider, slope of right side Add/Subtract after the bars: up and down

Graphing with transformations: To graph absolute value functions with transformations, we want to look from left to right. We will graph the transformations in that order.

Domain: Range:

Examples: Domain: Range: Domain: Range:

You Try – sketch the graphs of each of the following and give their domain and range:

Step Functions f(x) = [[x]] is the step function. [[ ]] indicates that its a Greatest Integer Function that rounds any number down to the nearest integer.

Greatest Integer Function F(x) = [[x]] (Pick the greatest integer less than or equal to the value) [[4.7]] = [[12.9]] = [[5]] =

Domain and Range Domain: Range:

f(x) = a[[x - h]] + k “a” term…negative flips… 0<a<1 vertical compression a<1 vertical shrink

f(x) = a[[x - h]] + k h  left and right (opposite of what you would think k  up and down f(x) = [[x – 5]]

Practice f(x) = 2[[x – 1]] + 2 f(x) = -[[x + 2]] - 3

Homework Worksheet