Transformations of Absolute Value Functions

This video tutorial covers the basics of absolute value functions, focusing on their graphing and transformations. It explains the V-shaped graph of absolute value functions and how to plot them using a table of values. The tutorial then delves into transformations, including stretching, compressing, and shifting, and how these affect the graph. It also covers reflections over the x and y axes. The video concludes with real-world applications of these transformations and a summary of the key points discussed.

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

• U-shaped

• S-shaped

• V-shaped

• W-shaped

What is the range of the parent function of an absolute value function?

• Only positive numbers

• From zero to positive infinity

• All real numbers

• From negative infinity to zero

What is the vertex of the parent function of an absolute value function?

• (1, 1)

• (0, 0)

• (0, 1)

• (-1, -1)

If the absolute value function is shifted to the left by 3 units, which part of the function changes?

• The sign of x

• The coefficient of x

• The constant inside the absolute value

• The constant outside the absolute value

What happens to the graph of an absolute value function when it is vertically stretched by a factor of 2?

• It shifts up by 2 units

• It shifts down by 2 units

• It becomes wider

• It becomes narrower

How do you describe a transformation that moves the graph of an absolute value function down by 5 units?

• Horizontal stretch

• Vertical stretch

• Horizontal shift

• Vertical shift

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

• Vertical stretch

• Horizontal stretch

• Reflection over the x-axis

• Reflection over the y-axis

If the function is f(x) = |x - 3| + 2, what transformation has been applied to the parent function?

• Shifted left 3 units and down 2 units

• Shifted right 3 units and down 2 units

• Shifted left 3 units and up 2 units

• Shifted right 3 units and up 2 units

In the function f(x) = 2|x|, what does the coefficient 2 represent?

• Horizontal compression

• Vertical stretch

• Vertical compression

• Horizontal stretch

In a real-world application, if the roof of a house is modeled by an absolute value function that is shifted 6 units to the right and 3 units up, what is the equation of the function?

• f(x) = |x + 6| + 3

• f(x) = |x - 6| + 3

• f(x) = |x + 6| - 3

• f(x) = |x - 6| - 3