Video: Identifying the Image of a Point on a Trigonometric Graph following a Transformation

The figure shows the graph of 𝑓(π‘₯). A transformation maps 𝑓(π‘₯) to 𝑓(π‘₯) βˆ’ 3. Determine the coordinates of 𝐴 following this transformation.

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Video Transcript

The figure shows the graph of 𝑓 of π‘₯. A transformation maps 𝑓 of π‘₯ to 𝑓 of π‘₯ minus three. Determine the coordinates of 𝐴 following this transformation.

When we look at the transformations of graphs, π‘Ž, β„Ž, and π‘˜ can transform it in a few ways. π‘Ž key there vertically stretch or compress it. β„Ž would move it horizontally left and right. And then π‘˜ moves it vertically up and down.

So since minus three is not on the inside of a parenthesis, that means the minus three must be a π‘˜. So since we’re subtracting three, so we will be moving down three. So 𝐴 is at 45, one. So if we need to go down three, here we’ll be going down one unit, now we’re at minus two units. And now we’ve subtracted three units. We’ve moved down three. So we are still at 45 for π‘₯. However, we are at negative two for 𝑦.

So after the transformation, the coordinates of 𝐴 would be 45, negative two.

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