Graphing Absolute Value Functions Explained

The video tutorial explains how to graph absolute value functions by hand, emphasizing the importance of identifying the vertex to accurately sketch the V-shape of the graph. It provides step-by-step instructions for graphing three examples, each with different vertex positions, and highlights the pattern recognition in the graphing process. The tutorial concludes with tips for ensuring accuracy and understanding the slope of the graph when no stretching or compressing is involved.

Why is it important to know the vertex when graphing absolute value functions?

• It helps in determining the y-intercept.

• It provides the highest point of the graph.

• It determines the slope of the graph.

• It helps in choosing appropriate x-values for a complete graph.

What is the general form of an absolute value function?

• f(x) = a|x - h| + k

• f(x) = ax + b

• f(x) = |x - h| + k

• f(x) = x^2 + bx + c

For the function f(x) = |x - 4| + 1, what is the vertex?

• (4, 1)

• (-4, -1)

• (-4, 1)

• (4, -1)

When graphing f(x) = |x - 4| + 1, what are the y-values for x = 2 and x = 6?

• 4 and 4

• 2 and 2

• 3 and 3

• 1 and 1

For the function f(x) = |x + 3|, what is the x-coordinate of the vertex?

• 3

• -3

• 0

• 1

What is the y-coordinate of the vertex for the function f(x) = |x + 3|?

• 0

• 1

• 3

• -3

For the function f(x) = |x| - 2, what is the vertex?

• (2, 0)

• (0, -2)

• (-2, 0)

• (0, 2)

What is the y-value for x = 1 in the function f(x) = |x| - 2?

• 2

• 0

• -1

• 1

What is the slope of each side of the V in an absolute value graph when there is no stretching or compressing?

• 0.5 and -0.5

• 3 and -3

• 1 and -1

• 2 and -2

What should you do if you are unsure about the points on an absolute value graph?

• Use a calculator to find the points.

• Always verify the points by substituting x-values.

• Skip the points and draw the graph directly.

• Guess the points based on the shape.