Graphing Absolute Value Functions

This video tutorial covers graphing absolute value functions, focusing on vertical and horizontal translations. It explains the characteristics of the parent function y = |x|, including its V-shape and symmetry. The tutorial demonstrates how to perform vertical translations by adjusting the value of K and horizontal translations by modifying H within the absolute value. It also discusses combining these translations and using the vertex to determine transformations from graphs.

What is the shape of the graph of an absolute value function?

• A circle

• A parabola

• A straight line

• A V-shape

What happens to the graph of y = |x| when you add a positive constant outside the absolute value?

• It shifts to the left

• It shifts down

• It shifts to the right

• It shifts up

If the equation is y = |x| - 5, how is the graph of y = |x| transformed?

• Shifted right 5 units

• Shifted left 5 units

• Shifted down 5 units

• Shifted up 5 units

In the equation y = |x - 4|, what does the -4 inside the absolute value indicate?

• Shift left 4 units

• Shift right 4 units

• Shift up 4 units

• Shift down 4 units

How does the graph of y = |x + 2| differ from y = |x|?

• Shifted left 2 units

• Shifted right 2 units

• Shifted down 2 units

• Shifted up 2 units

What is the vertex of the graph y = |x - 2| + 4?

• (-2, 4)

• (2, 4)

• (-2, -4)

• (2, -4)

For the function y = |x + 5| - 6, where is the vertex located?

• (-5, 6)

• (5, 6)

• (5, -6)

• (-5, -6)

If a graph is shifted to the left by 3 units and down by 7 units, what is the equation of the function?

• y = |x - 3| + 7

• y = |x + 3| - 7

• y = |x + 3| + 7

• y = |x - 3| - 7

What is the equation of a graph shifted to the right by 5 units and up by 1 unit?

• y = |x + 5| + 1

• y = |x + 5| - 1

• y = |x - 5| - 1

• y = |x - 5| + 1

How do you determine the equation of an absolute value function from its graph?

• By identifying the slope

• By measuring the length of the graph

• By finding the vertex and shifts

• By calculating the area under the curve