Vertex, Range, and Inequalities in Functions

This video tutorial focuses on graphing absolute value functions, covering key concepts such as the axis of symmetry, vertex, transformations, domain, and range. It provides step-by-step instructions for graphing functions like y = |x + 2| and y = |x - 3| + 1 using tables and transformations. The tutorial also explains how to graph absolute value functions with inequalities, including shading regions and determining whether to use solid or dashed lines.

What is the vertex of the function y = |x + 2|?

• (2, 0)

• (0, 2)

• (-2, 0)

• (0, -2)

Tags

CCSS.HSF-IF.C.7D

What is the axis of symmetry for the function y = |x + 2|?

• x = 2

• x = -2

• x = 0

• x = 1

For the function y = |x - 3| + 1, what is the range?

• [1, ∞)

• (-∞, 0]

• (-∞, 1]

• [0, ∞)

How does the graph of y = |x - 3| + 1 shift compared to y = |x|?

• 3 units right, 1 unit down

• 3 units left, 1 unit down

• 3 units right, 1 unit up

• 3 units left, 1 unit up

Tags

CCSS.HSF-IF.C.7D

What is the vertex of the function y = |x + 2| - 3?

• (2, -3)

• (-2, 3)

• (2, 3)

• (-2, -3)

Tags

CCSS.HSA.REI.D.12

For the inequality y ≥ -2|x - 1| + 4, where should the graph be shaded?

• Below the V

• Above the V

• Outside the V

• Inside the V

Tags

CCSS.HSF-IF.C.7A

What type of line is used for the inequality y ≥ -2|x - 1| + 4?

• No line

• Solid line

• Dashed line

• Dotted line

Tags

CCSS.HSF-IF.C.7D

What is the slope of the function y < 1/3|x + 1| - 2?

• 1/3

• -1/3

• 3

• -3

Tags

CCSS.HSF-IF.C.7D

Where should the graph be shaded for the inequality y < 1/3|x + 1| - 2?

• Above the graph

• Below the graph

• Inside the V

• Outside the V

Tags

CCSS.HSF-IF.C.7D

What is the vertex of the function y < 1/3|x + 1| - 2?

• (1, -2)

• (1, 2)

• (-1, 2)

• (-1, -2)

Tags

CCSS.HSF-IF.C.7D