Exploring Absolute Value Transformations

This video tutorial covers absolute value functions and their transformations. It begins with an introduction to the objectives, which include graphing absolute value functions by performing transformations on the parent function. The absolute value function is defined, and its graph is described as v-shaped and symmetric around the y-axis. The tutorial explains how translations shift the graph horizontally and vertically, and how stretching and shrinking affect the graph's shape. Techniques for graphing these functions without a table are demonstrated, emphasizing the importance of identifying the vertex and using slopes to plot points.

What is the parent function of an absolute value function?

• f(x) = 1/x

• f(x) = x

• f(x) = |x|

• f(x) = x^2

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

• (0, 0)

• (0, 1)

• (1, 0)

• (-1, -1)

How does the graph of an absolute value function compare to the linear parent function?

• It must always be positive

• It is identical

• It is always horizontal

• It is always negative

How does a translation affect the graph of an absolute value function?

• Reflects the graph across the x-axis

• Makes the graph narrower or wider

• Shifts the graph horizontally or vertically

• Changes its slope

How do you determine the new vertex after a translation?

• By moving h units horizontally and k units vertically from the origin

• By subtracting h and k from the original coordinates

• By moving h units to the right and k units up from the original vertex

• By adding h and k to the original coordinates

What does the 'h' value in a transformation indicate?

• Horizontal shift

• Vertical stretch

• Vertical shift

• Reflection across the y-axis

If the equation is 2| x - 1 | - 4, what is the new vertex?

• (-1, -4)

• (1, 4)

• (-1, 4)

• (1, -4)

What does a negative 'a' value do to the graph of an absolute value function?

• Reflects it across the x-axis

• Shifts it to the right

• Stretches it vertically

• Makes it wider

What effect does a value of 'a' greater than 1 have on the graph?

• It makes the graph wider

• It reflects the graph across the y-axis

• It shifts the graph to the right

• It makes the graph narrower

What does a 'shrink' in the context of absolute value function transformations refer to?

• The graph becoming wider

• A vertical stretch

• A horizontal shift

• A reflection across the x-axis