### Video Transcript

The function π 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 π of π₯ onto π of π₯ minus five. So, in our function up here π of
π₯, we need to replace π₯ with π₯ minus five. So, π of π₯ minus five is equal to
well, instead of π₯ in our first parentheses there, π₯ minus five, weβre gonna use
π₯ minus five. So, thatβs π₯ minus five minus
five. And again, in the next parentheses,
weβre replacing π₯ with π₯ minus five. So, that becomes π₯ minus five
minus two. And in the last parentheses again,
weβre 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, thatβs our answer. The question only said find an
equation. It didnβt tell us to multiply out
the parentheses and simplify it down. It just said find an equation. So, technically, weβd have got away
with this line here. But I think thatβs a little bit
cheeky. I think to tidy up a little bit to
this answer is probably preferable.