Question

Given the partially filled out table below for f(x), fill out the rest of it based on the function type

Answer 1

Part A:

Given the partially filled out table below for an even function f(x)

$\begin{tabular} {|c|c|c|c|c|c|c|c|} x&-3&-2&-1&0&1&2&3\\[1ex] y&5&&-7&4&&-4&& \end{tabular}$

For an even function f(x) = f(-x)

Thus, From the table f(-2) = f(2) = -4, thus the missing y-value for x = -2 is -4.
f(1) = f(-1) = -7, thus the missing y-value for x = 1 is -7.
And f(3) = f(-3) = 5, thus the missing y-value for x = 3 is 5.



Part B:

Given the partially filled out table below for an odd function f(x)

$\begin{tabular} {|c|c|c|c|c|c|c|c|} x&-3&-2&-1&0&1&2&3\\[1ex] y&5&&-7&0&&-4&& \end{tabular}$

For an odd function f(-x) = -f(x)

Thus, From the table f(-2) = -f(2) = -(-4) = 4, thus the missing y-value for x = -2 is 4.
f(-1) = -f(1) ⇒ -7 = -f(1) ⇒ f(1) = 7, thus the missing y-value for x = 1 is 7.
And f(-3) = -f(3) ⇒ 5 = -f(3) ⇒ f(3) = -5, thus the missing y-value for x = 3 is -5.