Precalculus Question

Question

Decide which of the following properties apply to the function. (More than one property may apply to the function. Select all that apply.)

y = ln(|x|)

The range of the function is (−∞, ∞).The function is one-to-one.The function has a turning point.The function is decreasing for −∞ < x < ∞.The domain of the function is (−∞, ∞).The graph has an asymptote.The function is increasing for −∞ < x < ∞.The function is a polynomial function.

Answer 1

Let's graph y = ln(|x|)

The range of the function is (−∞, ∞). Yes, sure looks like any y value is attainable

The function is one-to-one. No. Does not pass the horizontal line test

The function has a turning point. I don't see any turning points

The function is decreasing for −∞ < x < ∞. I see it decreasing from −∞ to 0 but then it increases from 0 to ∞

The domain of the function is (−∞, ∞). No, x = 0 is not in the domain

The graph has an asymptote. Yes at x = 0

The function is increasing for −∞ < x < ∞. No, decreasing from −∞ to 0

The function is a polynomial function. No, a polynomial looks like c₁xⁿ + c₂x^n-1 + c₃x^n-2 + . . .