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

https://www.desmos.com/calculator/op6ldnjfls

Answer 2

\[\left| x \right|\ge 0\]
\[\left| x \right|+3 \ge3\]
so \[f(x)\ge 3\]
Hence \[ Range \ge 3 \]

Answer 3

The range of the function f(x) = |x| + 3 is:

{f(x) ∈ ℝ | f(x) ≥ 3}

The absolute value of x is always non-negative, so the value of |x| is always greater than or equal to 0. Adding 3 to |x| gives a range of values that is greater than or equal to 3. Therefore, the range of the function is all real numbers such that f(x) is greater than or equal to 3.

Answer 4

YOUR BIG HEAD