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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 \: \: \: \: \: \: \: \:

This graph shows a portion of and even function. Use the graph to complete the table-example-1
This graph shows a portion of and even function. Use the graph to complete the table-example-1
This graph shows a portion of and even function. Use the graph to complete the table-example-2

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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}

This graph shows a portion of and even function. Use the graph to complete the table-example-1
User Mandulaj
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