State whether each function is a linear function. Explain.
1 answer:
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Answer:
The domain is all real numbers and the range is non-negative real numbers
(y ≥ 0) ⇒ answer B
Step-by-step explanation:
* Lets revise the parent function of the absolute value
- The absolute value or modulus |x| of a real number x is the
non-negative value of x
- The absolute value of a number means the magnitude of the number
without regard to its sign
- The parent function of the absolute value is f(x) = IxI
∵ The domain of the function is all the values of x which make the
function defined
∵ In the function f(x) = IxI, x can be any number
∴ The domain of the f(x) is any real number
∴ The domain is (-∞ , ∞) or {x : x ∈ R}
∵ The range is the set of values of y that corresponding with the
domain
∵ f(x) = IxI is non-negative value
∴ f(x) ≥ 0
∵ f(x) = y
∴ y ≥ 0
∴ The range is the set of real numbers greater than or equal zero
∴ The range is [0 , ∞) or {y : y ≥ 0}
* The true statement is: The domain is all real numbers and the range is
non-negative real numbers (y ≥ 0)
