Question

identify the collection of three functions which all have a domain of (-∞,∞).
choose the correct answer.
a. y = \frac{1}{x}, y = x, and y = \sqrt3{x}
b. y = |x|, y = \frac{1}{x}, and y = x^{3}
c. y = x^{3}, y = x^{2}, and y = |x|
d. y = x^{3}, y = 3, and y = \sqrt{x}

Explanation:

Step1: Recall domain rules

The domain of $y = \frac{1}{x}$ is $x
eq0$, so options A and B are incorrect as they contain $y=\frac{1}{x}$. The domain of $y = \sqrt{x}$ is $x\geq0$, so option D is incorrect as it contains $y=\sqrt{x}$.

Step2: Analyze option C

For $y = x^{3}$, any real - number $x$ can be cubed. For $y=x^{2}$, any real - number $x$ can be squared. For $y = |x|$, any real - number $x$ can have its absolute value taken. All three functions in option C have a domain of $(-\infty,\infty)$.

Answer:

C. $y = x^{3},y = x^{2}$, and $y = |x|$