Final answer:
The question focuses on the mathematics subject, specifically the properties of the absolute value function, y = |x|, which is an even function.
Step-by-step explanation:
The student's question on the function y = |x| pertains to understanding the properties of absolute value functions. This function represents an even function, which is symmetric about the y-axis. By definition, an even function satisfies the condition that y(x) = y(-x), meaning the function's value at x is the same as its value at -x. The graph of y = |x| can be produced by plotting specific values for (x,y) data pairs, revealing a V-shaped graph that intersects the origin (0,0).
It's important to note that certain functions can have limitations such as asymptotes, as exemplified by the function y = 1/x mentioned in FIGURE 4.4. However, the absolute value function does not have asymptotes, since it is defined for all real numbers and only touches the x-axis at the origin.
In terms of properties of functions, it’s also useful to remember translation transformations. For instance, f(x-d) would translate the function in the positive x-direction by a distance d, while f(x+d) would translate it in the negative x-direction by the same distance. Translations do not affect the even or odd nature of a function but shift its position on the graph.