Question Video: Finding the Transformed Function in the Direction of the Positive π‘₯-Axis Mathematics

The function 𝑓(π‘₯) = (π‘₯ βˆ’ 5)(π‘₯ βˆ’ 2)(π‘₯ + 7) is translated +5 units in the direction of the positive π‘₯-axis. Find an equation for the transformed function.

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Video Transcript

The function 𝑓 of π‘₯ equals π‘₯ minus five times π‘₯ minus two times π‘₯ plus seven is translated positive five units in the direction of the positive π‘₯-axis. Find an equation for the transformed function.

Well, to translate positive five units in the π‘₯-direction, we need to map 𝑓 of π‘₯ onto 𝑓 of π‘₯ minus five. So, in our function up here 𝑓 of π‘₯, we need to replace π‘₯ with π‘₯ minus five. So, 𝑓 of π‘₯ minus five is equal to well, instead of π‘₯ in our first parentheses there, π‘₯ minus five, we’re gonna use π‘₯ minus five. So, that’s π‘₯ minus five minus five. And again, in the next parentheses, we’re replacing π‘₯ with π‘₯ minus five. So, that becomes π‘₯ minus five minus two. And in the last parentheses again, we’re gonna replace π‘₯ with π‘₯ minus five. So, now, all we have to do is tidy up those parentheses.

Well, the first one, π‘₯ minus five minus another five is π‘₯ minus 10. And in the second one, π‘₯ minus five minus another two is π‘₯ minus seven. And in the last one, π‘₯ minus five plus seven is π‘₯ plus two. So, in fact, that’s our answer. The question only said find an equation. It didn’t tell us to multiply out the parentheses and simplify it down. It just said find an equation. So, technically, we’d have got away with this line here. But I think that’s a little bit cheeky. I think to tidy up a little bit to this answer is probably preferable.

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