Question

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This graph shows a portion of an even function.
Use the graph to complete the table of values.
6
f(x)
-1
4
-3
-5
-6
2
DONE
2
4.
6

Answer 1

Answers:

• first box = 1
• second box = 1
• third box = 3
• fourth box = 3

Refer to the graph below.

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Explanation:

If f(x) is an even function, then f(-x) = f(x) for all x in the domain.

What this means is that we have symmetry about the y axis. We can reflect that given curve over the y axis to generate the missing left side.

The graph shows that (1,1) is on the orange curve. It reflects over to (-1,1). This means 1 goes in the first box.

Use the rule $(x,y) \to (-x,y)$ to apply a y axis reflection. We simply just change the sign of the x coordinate from positive to negative, while keeping the y coordinate the same.

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We can also see that (3,1) is also on the orange curve. It reflects over to (-3, 1) using that rule mentioned earlier.

1 goes in the second box

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The graph your teacher gave you shows that if we plugged in x = 5, then we get y = 3. In other words, the point (5,3) is on the orange graph.

It reflects over to (-5, 3) to show that x = -5 leads to the output y = 3

3 goes in the third box

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Lastly, the point (6,3) reflects to (-6,3) when reflecting over the y axis.

3 goes in the fourth box.

See the graph below.