An input to a system can often be described by commonly seen mathematical functions. For each of the functions below, sketch the graph of the function and state whether it is an odd function, an even function, or neither of the two. (1) $f_{1} (x) = 15$ (2) $f_{2} (x) = 3 x^{2}$ (3) $f_{3} (x) = f_{1} (x) + f_{2} (x)$ (4) $f_{4} (x) = 2 x^{3}$ (5) $f_{5} (x) = f_{1} (x) + f_{4} (x)$ From the above, comment on how the addition of a constant function to an odd or even function will affect the resulted function being odd or even (or neither of the two).

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An input to a system can often be described by commonly seen mathematical functions. For each of the functions below, sketch

An input to a system can often be described by commonly seen mathematical functions. For each of the functions below, sketch the graph of the function and state whether it is an odd function, an even function, or neither of the two. (1)

f_{1} (x) = 15

(2)

f_{2} (x) = 3 x^{2}

(3)

f_{3} (x) = f_{1} (x) + f_{2} (x)

(4)

f_{4} (x) = 2 x^{3}

(5)

f_{5} (x) = f_{1} (x) + f_{4} (x)

From the above, comment on how the addition of a constant function to an odd or even function will affect the resulted function being odd or even (or neither of the two).

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