Thread: Wondering if someone can help me out by marking a few questions I've done - Functions

I've done all the questions (I think), and I don't really get detailed info back from my teachers in this course, so I was hoping somebody could mark these for me, and tell me what I've done wrong, and why, and how I can fix it. It's a little unorthodox, I suppose, but I'd really appreciate the help. All the questions are attached to this post in .doc format.

Thanks so much!

Hey OverlyFrustrated.

For Lesson 8, Just a few minor mistakes (possibly typos): (1,3/5) should be (-1,3/5) in column 2 and you should have -5.-4,-3,-2,-1 as your new X values. Also (3,-125) should be (3,-375) as well as (-3,2/5) should be (-5,7/5).

Your thinking is correct though for that lesson but you got quite a few errors in the final numerical answer.

Lesson 7 looks pretty good.

For Lesson 9 (the very last question), recall that if you have y = a^x then log_a(y) = x where log_a(y) = ln(y)/ln(a) and log_a is the logarithm in base a (if it exists).

This will give you an exact answer and a good enough approximation on the calculator without needing trial or error.

Hi Chiro!

Thanks so much for the help!

One issue I have is that we haven't learned logarithms yet. I could go about learning what they are and how to use them, but I think they fall outside of the course where it is currently, unfortunately. This is a problem I seem to be encountering a lot, but alas.

Logarithms have these major properties:

log(xy) = log(x) + log(y) for any valid logarithm in a valid base (got to be > 0 and not 1) and
log(x/y) = log(x) - log(y)
log(x^a) = alog(x)

This is basically it for defining a logarithm: if it has these properties and is well defined then it's a logarithmic function.

The change of base formula allows you to got from one base to another and the formula is log_b(x) = log(x)/log(b) where log_b is in base b and log is in some other base (usually the natural logarithm).

You can prove a lot of other stuff and properties, but they are basically taking those statements to get new ones.

Thanks a bunch for the tips!

Unfortunately I can't use logarithms to answer these questions and still get marks .

Chiro, sorry, one last question: where should I have -4,-4,-3,-2,-1, for my x values? I graphed y=-3(5^x) and the values I got seemed accurate.