Absolute Value Functions and Transformations

The video tutorial explores the absolute value function f(x) = |x - 4| - 3, using Desmos software to graph it. Key attributes such as domain, range, vertex, axis of symmetry, and intercepts are identified. The domain is all real numbers, while the range is from -3 to positive infinity. The vertex is at (4, -3), serving as the minimum point. The axis of symmetry is x = 4. The x-intercepts are at (1, 0) and (7, 0), and the y-intercept is at (0, 1). The tutorial also discusses transformations to find the vertex without a graph.

What software was used to graph the absolute value function?

• GeoGebra

• Desmos

• Wolfram Alpha

• GraphCalc

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

• S-shape

• W-shape

• V-shape

• U-shape

What is the domain of the absolute value function f(x) = |x - 4| - 3?

• x ≥ 0

• All real numbers

• x ≤ 0

• x ≠ 0

Why is the domain of the absolute value function all real numbers?

• Because it is a linear function

• Because it has no restrictions on x

• Because it is a constant function

• Because it is a quadratic function

What is the range of the function f(x) = |x - 4| - 3?

• y < 0

• y > 0

• y ≤ -3

• y ≥ -3

What is the minimum value of the function f(x) = |x - 4| - 3?

• -3

• 0

• -4

• 3

Where is the vertex of the function f(x) = |x - 4| - 3 located?

• (4, -3)

• (0, 4)

• (4, 0)

• (0, -3)

Is the vertex of the function f(x) = |x - 4| - 3 a maximum or minimum?

• Both

• Maximum

• Minimum

• Neither

What is the axis of symmetry for the function f(x) = |x - 4| - 3?

• x = 0

• x = 4

• x = -4

• x = 3

How does the axis of symmetry relate to the graph of an absolute value function?

• It divides the graph into two unequal parts

• It is not related to the graph

• It is a horizontal line

• It acts as a mirror line