Question

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

{f(x) ∈ ℝ | f(x) ≤ 3}
{f(x) ∈ ℝ | f(x) ≥ 3}
{f(x) ∈ ℝ | f(x) > 3}
{f(x) ∈ ℝ | f(x) < 3}

Answer 1

{f(x) ∈ ℝ | f(x) ≥ 3}  is the range of f(x) = |x| + 3

⇒ Range is in the y-axis

When graphing the following equation shown below:

• f(x) ≥ 3

• f(x) ∈ ℝ

• [ 3, ∞ ]

Answer 2

Answer:

{f(x) ∈ ℝ | f(x) ≥ 3}

Step-by-step explanation:

The range of a function is the output values (y-values).

Absolute value is the distance of x from zero, so it is never negative.  It is denoted by a bar on either side of the term.

Therefore, as |x| ≥ 0 then |x| +3 ≥ 3

Therefore, the range of the function is {f(x) ∈ ℝ | f(x) ≥ 3}