Which of the following functions has a graph that is symmetric about the $y$-axis?
Select all that apply.
A. $y=\frac{1}{x}$
B. $y=x^{3}$
C. $y=\sqrt{x}$
D. $y=|x|$
Final Answer: The function that is symmetric about the y-axis is \(\boxed{D. y=|x|}\).
Step 1 :A function is symmetric about the y-axis if and only if f(x) = f(-x) for all x in the domain of f. We can check each of the given functions to see if they satisfy this property.
Step 2 :Check function A: $y=\frac{1}{x}$. It does not satisfy the condition f(x) = f(-x) for all x in the domain of f, so it is not symmetric about the y-axis.
Step 3 :Check function B: $y=x^{3}$. It is only symmetric at x=0, so it is not symmetric about the y-axis.
Step 4 :Check function C: $y=\sqrt{x}$. It is only symmetric at x=0, so it is not symmetric about the y-axis.
Step 5 :Check function D: $y=|x|$. It satisfies the condition f(x) = f(-x) for all x in the domain of f, so it is symmetric about the y-axis.
Step 6 :Final Answer: The function that is symmetric about the y-axis is \(\boxed{D. y=|x|}\).