Graphing Absolute Value Functions in Algebra

This video tutorial covers algebra lesson 5-8 on graphing absolute value functions. It begins with an introduction to absolute value functions, explaining their v-shaped graphs. The lesson then explores graph translations, both horizontal and vertical, and introduces piecewise and step functions. The tutorial includes detailed examples of graphing absolute value equations and explains how to perform horizontal and vertical translations. A practical example of a step function is provided using a scenario involving buses and students. The lesson concludes with a closure question summarizing the key concepts.

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

• A circle

• A parabola

• A V-shape

• A straight line

What is a piecewise function?

• A function with a single rule for all values

• A function that only has positive values

• A function with different rules for different parts of its domain

• A function that is always increasing

How does the graph of y = |x| + k translate?

• Upward by k units

• Right by k units

• Downward by k units

• Left by k units

What is the y-intercept of the parent function y = |x|?

• (0, 1)

• (1, 1)

• (1, 0)

• (0, 0)

If the equation is y = |x| - 4, how is the graph translated?

• Right by 4 units

• Left by 4 units

• Downward by 4 units

• Upward by 4 units

How does the graph of y = |x + h| translate?

• Left by h units

• Right by h units

• Downward by h units

• Upward by h units

What happens to the graph of y = |x - h|?

• It shifts left by h units

• It shifts right by h units

• It shifts up by h units

• It shifts down by h units

In the equation y = |x - 3| - 4, how is the graph translated?

• Left 3 units and up 4 units

• Right 3 units and down 4 units

• Left 3 units and down 4 units

• Right 3 units and up 4 units

What is a step function?

• A function that has a continuous graph

• A function that only decreases

• A function that pairs every number in an interval with a single value

• A function that only increases

How many buses are needed for 120 students in a step function scenario?

• 1 bus

• 2 buses

• 3 buses

• 4 buses