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QuestionIf (3,−18)(3,-18) is on an odd function's graph, what other point must also be on the graph?

Studdy Solution

STEP 1

Assumptions1. The point (3,−18)(3,-18) is on the graph of an odd function. . An odd function is a function that satisfies the property f(−x)=−f(x)f(-x) = -f(x) for all xx in the domain of ff.

STEP 2

We can use the property of odd functions to find another point that is guaranteed to be on the graph. The property of odd functions is f(−x)=−f(x)f(-x) = -f(x).

STEP 3

We know that the point (3,−18)(3,-18) is on the graph, so we can write this as f(3)=−18f(3) = -18.

STEP 4

Now, we can use the property of odd functions to find the yy-coordinate when x=−3x = -3. According to the property, f(−3)=−f(3)f(-3) = -f(3).

STEP 5

Substitute f(3)=−18f(3) = -18 into the equation to find f(−3)f(-3).
f(−3)=−f(3)=−(−18)f(-3) = -f(3) = -(-18)

STEP 6

Calculate the value of f(−3)f(-3).
f(−3)=−(−18)=18f(-3) = -(-18) =18So, the point (−3,18)(-3,18) is guaranteed to be on the graph of the function.

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