Final answer:
A function is even if its graph is symmetric about the y-axis and odd if it is symmetric about the origin. A graphing calculator like the TI-83, 83+, or 84 can be used to check the graph's symmetry and determine if a function is even, odd, or neither. The correct answer from the options will depend on this visual assessment.
Step-by-step explanation:
To determine if a function is even, odd, or neither using a calculator, you should understand the properties of even and odd functions. An even function satisfies the property f(-x) = f(x) for all x in the function's domain, which means that the graph of the function is symmetric with respect to the y-axis. An odd function satisfies the property f(-x) = -f(x) for all x in the function's domain, indicating symmetry with respect to the origin.
If using a graphing calculator like the TI-83, 83+, or 84, you can graph the function and visually determine if the graph shows the respective symmetry. If the graph is symmetric with respect to the y-axis, it's an even function; if it's symmetric with respect to the origin, it's an odd function. If it shows no symmetry, the function is neither even nor odd.
Remember that a function cannot be both even and odd, so 'Both even and odd' is not a valid answer. To find the correct answer from the options A) Even, B) Odd, C) Neither, D) Both even and odd, observe the symmetry of the function's graph using the calculator.