Graphing Absolute Value Functions: Range and Domain Insights

This video tutorial by M2 covers graphing absolute value functions, identifying their domain and range, and understanding transformations. It explains how absolute value functions are shaped like a V and discusses the effects of various transformations such as moving left, right, up, down, and reflecting over axes. The tutorial also covers how to determine the domain and range of these functions, emphasizing that the domain is all real numbers and the range depends on the vertex. Advanced graphing techniques are also explored, including the impact of vertical stretching and flipping over the x-axis.

What shape does an absolute value function typically have?

• S-shape

• W-shape

• U-shape

• V-shape

Which transformation moves the graph of an absolute value function to the right?

• Adding a constant outside the absolute value

• Subtracting a constant outside the absolute value

• Subtracting a constant inside the absolute value

• Adding a constant inside the absolute value

If the vertex of an absolute value function is at (3, 4), what is the equation of the function?

• |x - 3| - 4

• |x + 3| + 4

• |x + 3| - 4

• |x - 3| + 4

What is the domain of an absolute value function?

• All integers

• All real numbers

• All positive numbers

• All negative numbers

How is the range of an absolute value function determined?

• By the x-values

• By the y-values

• By the slope

• By the intercept

What does a negative sign in front of the absolute value function indicate?

• Reflection over the x-axis

• Reflection over the y-axis

• Horizontal stretch

• Vertical stretch

If an absolute value function is vertically stretched by a factor of 2, how does it affect the graph?

• It becomes narrower

• It shifts up

• It shifts down

• It becomes wider

For the function -2|x + 1| - 5, where is the vertex located?

• (-1, -5)

• (1, -5)

• (-1, 5)

• (1, 5)

What is the range of the function -2|x + 1| - 5?

• y ≥ -5

• y ≤ -5

• y ≥ 5

• y ≤ 5

What is the ratio used to determine the slope of an absolute value function?

• 2:1

• 1:1

• 3:1

• 1:2