Question

Math 2 Homework Mod 2.1 (Day 2) Absolute Value Functions

Answer 1

The descriptions of the transformations are:

• Vertex: (-6, 0)
• Stretch factor: 2
• Domain: set of all real numbers
• Range: set of real numbers greater than or equal to 0

How to describe transformations, graph, and state domain & range using any notation?

The function is given as:

f(x) = -2|x + 6|

The above function is an absolute value function, and an absolute value function is represented as:

f(x) = a|x - h| + k

Where

Vertex = (h, k)

Scale factor = a

So, we have:

a = -2

(h, k) = (-6, 0)

There is no restriction to the input values.

So, the domain is the set of all real numbers

The y value in (h, k) = (-6, 0) is 0

i.e.

y = 0

Because the factor is negative (-2), then the vertex is a minimum

So, the range is all set of real numbers greater than or equal to 0

Hence, the descriptions of the transformations are:

• Vertex: (-6, 0)
• Stretch factor: 2
• Domain: set of all real numbers
• Range: set of real numbers greater than or equal to 0

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