Mth 163
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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I am practicing some of the major quiz problems and I have come across this type of function. If f(x) = x^2, give the vertex and the three basic points of the graphs of f(x--.75), f(x) - -.15, .2 f(x) and .2 f(x--.75) + -.15. Quickly sketch each graph. would you please explain what this means? The x-- thing is throwing me off
(x - -.75) means you are subtracting -.75 from x.
The result is therefore x + .75.
I use the - - instead of + to emphasize that replacing x by x - h shifts the vertex h units. So replacing x by x - -.75 shifts the vertex -.75 units. Of course this is the same as replacing x by x + .75.
Similarly an expression like f(x) + -1.25 (which doesn't actually occur in the problem you're asking about) would be the same as f(x)-1.25. I would write it as f(x) + -1.25 to emphasize that the vertical shift, which has form f(x) + k, would in this case by -1.25.
The expressions in the problem you quote could as well have been written f(x+.75), f(x) + .75, .2 f(x + .75) - .15.