Exploring Absolute Value Graphs

The video tutorial covers the concept of absolute value functions, focusing on their v-shaped graphs. It explains how to graph these functions without creating a table by using translation rules. The tutorial demonstrates how these rules apply to various functions, including shifts and translations both horizontally and vertically. Through examples, it illustrates the application of these rules, making it easier to understand graph transformations. The video concludes with a review of the key concepts and techniques discussed.

What is the shape of the graph of an absolute value function?

• A straight line

• A parabola

• A V-shape

• A circle

What does the absolute value function do to negative inputs?

• Changes them to positive

• Keeps them negative

• Squares them

• Cubes them

What is the purpose of translation rules in graphing absolute value functions?

• To change the shape of the graph

• To shift the graph horizontally or vertically

• To rotate the graph

• To reflect the graph over the x-axis

How does the graph of y = |x| change when it is shifted 2 units down?

• It moves 2 units down

• It moves 2 units up

• It moves 2 units to the right

• It moves 2 units to the left

What happens to the graph of y = |x| when it is shifted 5 units to the left?

• It moves 5 units down

• It moves 5 units up

• It moves 5 units to the left

• It moves 5 units to the right

What is the new vertex of the graph y = |x + 4|?

• (0, 4)

• (0, -4)

• (4, 0)

• (-4, 0)

If the equation of the graph is y = |x| + 3, how is the graph shifted?

• 3 units up

• 3 units down

• 3 units to the left

• 3 units to the right

What is the effect of a negative sign inside the absolute value function, such as y = |x - 2|?

• Shifts the graph 2 units down

• Shifts the graph 2 units up

• Shifts the graph 2 units to the right

• Shifts the graph 2 units to the left

How do you determine the new vertex of the graph y = |x - 3| + 2?

• (3, 2)

• (-3, 2)

• (-3, -2)

• (3, -2)

What is the general effect of adding a constant outside the absolute value function, such as y = |x| + c?

• Dilates the graph

• Shifts the graph horizontally

• Reflects the graph

• Shifts the graph vertically