This graph shows a portion of and even function. Use the graph to complete the table of values. What are the values of f(x)?\: \: \: \: \: \: \: \: \: \: \: \: \: x \: \: \: \: …

Question

This graph shows a portion of and even function. Use the graph to complete the table of values. What are the values of f(x)?
`\: \: \: \: \: \: \: \: \: \: \: \: \: x \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: f(x) \\ - 1 \: \: \: \: \: \: \: \: \\ - 3 \: \: \: \: \: \: \: \: \\ - 5 \: \: \: \: \: \: \: \: \\ - 6 \: \: \: \: \: \: \: \:`

Answer 1

To find the values of f(x) at each given value of x, draw a vertical line on each given value of x and check which value of y corresponds to that value of x using the graph of f(x).

The problem says that the function is an even function. This means that:

`f(x)=f(-x)`

Then, the function for negative values of x is the same that the function evaluated on the corresponding positive values.

For x=-1, we know that:

`f(-1)=f(1)`

From the graph, we can see that f(1)=1

Repeating this procedure for x=-3, -5 and -6 we find that:

`\begin{gathered} f(-1)=f(1)=1 \\ f(-3)=f(3)=1 \\ f(-5)=f(5)=3 \\ f(-6)=f(6)=3 \end{gathered}`