Question

This graph shows a portion of an odd function,6Use the graph to complete the table of valuesx-2fix)-3-4-6DONE►3 of 7

Answer 1

First, we must take into account the definition of an odd function. A function f(x) is an odd function if it has the following property for all values of x:

$f(-x)=-f(x)$

We can use this property to solve the exercise.

From the graph we read the following values for f:

$\begin{gathered} f\mleft(2\mright)=2 \\ f\mleft(3\mright)=1 \\ f\mleft(4\mright)=2 \\ \mleft(6\mright)=3 \end{gathered}$

Using the data above and the property that defines odd functions we find:

$\begin{gathered} f(-2)=-f\mleft(2\mright)=-2 \\ f(-3)=-f\mleft(3\mright)=-1 \\ f(-4)=-f\mleft(4\mright)=-2 \\ f(-6)=-f\mleft(6\mright)=-3 \end{gathered}$

Answer

x f(x)

-2 -2

-3 -1

-4 -2

-6 -3