Graphing Absolute Value Functions

The video tutorial explains how to model the roof of a birdhouse using the function f(x) = -5|x| + 10, focusing on graphing absolute value functions. It covers the concept of absolute value, common misunderstandings, and how to graph these functions using a t-chart. The tutorial also demonstrates graphing the birdhouse roof function, highlighting its upside-down V shape due to the negative coefficient, and determining the roof's vertical height and horizontal base distance.

What is the function used to model the roof of the birdhouse?

• f(x) = 5|x| + 10

• f(x) = -5x + 10

• f(x) = -5|x| + 10

• f(x) = 5x + 10

What is the absolute value of -4?

• 0

• -4

• 4

• 8

If x = -2, what is the correct way to substitute it into the expression |3 - x|?

• |3 - (-2)|

• |3 - 2|

• |3 + (-2)|

• |3 + 2|

What shape does the graph of an absolute value function typically have?

• U-shaped

• V-shaped

• S-shaped

• L-shaped

Where is the vertex of the graph of the function |x| located?

• (2, 2)

• (-1, -1)

• (1, 1)

• (0, 0)

What is the effect of a negative sign in front of the absolute value function?

• It makes the graph a straight line.

• It inverts the graph to an upside-down V.

• It shifts the graph downwards.

• It shifts the graph upwards.

What is the vertical height of the birdhouse roof?

• 5 feet

• 8 feet

• 10 feet

• 12 feet

What is the horizontal distance at the base of the birdhouse roof?

• 3 feet

• 4 feet

• 5 feet

• 2 feet

What is the purpose of using a t-chart in graphing absolute value functions?

• To find the slope of the line

• To determine the vertex of the graph

• To organize x and y values for plotting

• To calculate the area under the curve

What have you learned in this lesson about graphing absolute value functions?

• How to find the area of a triangle

• How to calculate derivatives

• How to graph using a t-chart

• How to solve quadratic equations