Warm-up

Use desmos to create an absolute value function with a vertex of (3,2)

Copy and Paste your function below.

Based on the above examples of vertical shift.

How is the graph of y = |x| + 2 related to the graph of its parent function y = |x|?

Based on the above examples of vertical shift.

How is the graph of y = |x| - 7 related to the graph of its parent function y = |x|?

Based on the above examples of horizontal shift.

How is the graph of y = |x - 8| related to the graph of its parent function y = |x|?

Based on the above examples of horizontal shift.

How is the graph of y = |x+2| related to the graph of its parent function y = |x|?

Based on the above examples of stretch and compression.

How is the graph of y = 2|x | related to the graph of its parent function y = |x|?

Based on the above examples of stretch and compression.

How is the graph of y = ¼|x | related to the graph of its parent function y = |x|?

What is the vertex of the function:

Based of the parent function, f(x)=|x|,

is this function stretched or compressed by a factor 3?

What is the vertex of the function:

Based of the parent function, f(x)=|x|,

is this function stretched or compressed by a factor 5?

Use desmos to graph f(x) and g(x)

What is the vertex of g(x)?

Describe how g(x) been transformed from the original function f(x)

Find the vertex of the absolute value function:

Graph the absolute value function:

Be sure to label the vertex from question #14 and use it as the center of your graph.

Based on the above example of reflection.

How does the "v" graph the of y = - 2|x | open?

Based on the above example of reflection.

How does the "v" graph the of y = ½|x | open?

Match each absolute value equation with its graph.

Match each absolute value equation with its graph.

Graph the absolute value function:

Be sure to label the vertex and use it as the center of your graph.

Graph the absolute value function:

Be sure to label the vertex and use it as the center of your graph.

Graph the absolute value function:

Be sure to label the vertex and use it as the center of your graph.

Use the graph to create a function with the following features:

1) As x gets smaller; the function approaches negative infinity.

x→ - ∞; f(x)→- ∞

2) As x gets larger; the function approaches negative infinity.

x→ ∞; f(x)→ -∞

3) The graph of the function passes through the x-axis at 4.

Is this an open or closed interval?

The definition of absolute value is...

Simplify:

Show your work for credit.