Review Problems

Somebody sez Brutus is absent today for good reason & she’s been asked to take the notes. Which is a bunch of exercises. And Brutus reads the blog. So here goes, quick and dirty.

1. The order of transformations matters. Demonstrate this by graphing the “original” graph y = | x| , then (i) Shift up 2, then reflect in the x axis; and (ii) Reflect in x axis, then shift up 2.

2.Write a definition for the piecewise function on the blackboard. Sorry. Not ready to try to draw it here. Piecewise-linear if that’s any help. (Part of the point here is that both directions — graphics to algebra and algebra to graphics — make good exercises. We had the other one on the quiz.)

3. Give (exactly — e.g. 32/113, not .3274) both co-ordinates for the vertex of y = -17x^2 +11x + 5.

4.The Demand function for a certain product is p = 100 – .2 x. (a) Determine the Revenue function. (b)Find the maximum revenue. (c) What are the quantity and price that give this revenue?

Also covered (though not here): anything from the first 2 quizzes (domain & range; increasing & decreasing; intercepts; maxes and mins [nonquadratic]; symmetries …)


  1. ellie

    1) will the step functions be on the test?

    2)to find the vertex with fractions instead of decimal points [you’re killing me here btw] can we find it with decimal points first and then switch it to fractions via the calculator?

  2. brutus12

    Well i’m just getting in and figured i would see what i missed and that pretty much explains it. Thanks so much for the update and posting that information!! :-)

  3. @ellie

    1) step functions are supposed to be
    “fair game” … but we’ve had very little
    actual practice with ’em …
    so *if* i put one on the exam
    (that i’m about to finalize),
    it’ll be in some inessential way
    (like “what transformation changes
    int(x) to -int(x)”; the student answers
    “reflection in the x axis”; this is a
    problem about *transformations*,
    not the “int” function … any other
    function would have done just as well).

    2) the “Frac” feature of the calculator
    is indeed the tool of choice for
    “exact co-ordinates”.

    “plug in” the x co-ordinate of the vertex
    (found via “H = -B/(2A)”) on the formula
    (previously loaded into the Y_1 function
    of the calculator, say); evalaluate; use
    the “Frac”.

    probably one should compute by hand
    and use the calculator to check just for practice
    (when working such problems at leisure;
    under exam conditions, verifying everything
    right on the calculator is faster (and exams
    are no time for “practice”!).

    anyway, that’s what i like to do in class.
    most algebra students can sure *use* the practice
    (in rational number arithmetic — “manipulating fractions”).

    somebody asked me about this topic
    in one-to-one work in the 10:00
    and i realized we’d never done
    any in-class work with the Frac feature.
    it’s still a good problem but might
    call for a hint …

    @ brutus
    see you in a couple hours … well prepared i hope!

  4. brutus12

    pheww soo much for the well prepared on the revenue problem, number 4 i think. Dang it!! For some reason i drew a blank, decided i’d go back to it at the end and with just minutes left before my next class, that i had to give a speech in, i had to throw in the towl. Let’s just say i’m pissed, i never leave problems blank or give up!! Anyway the review helped alot to prepare for the test and the clarity of the questions were great. Between all the madness going on with the 19credit hours im taking this quarter, im actually learning some math, and you can bet that revenue exercises will NOT be an issue again, i’ll be able to do em’ in my sleep.

  5. for anybody not in the class:
    usually the main problem with problems
    like my number 4 is the first step:
    we require that the student know
    that “R = xp” —
    revenue is number-sold times price-per-item —
    so that, for example, one has
    R(x) = 100x – .2x^2
    in the stated problem.
    once the right quadratic function is made explicit,
    everything else tends to fall into place.
    or anyway, there are all *kinds* of issues
    that may arise *after* this step;
    the trouble is that *without* this step,
    one can’t even really get properly started.
    so “not getting started” is unfortunately
    the commonest error on problems like this.

    it appears to be just the kind of thing
    that we teachers are more-or-less *supposed*
    to require students to know … so i try to stress
    the importance of this step in at least two classroom
    presentations before a test …

    note that the actual *math* involved here
    amounts to little more than “common sense”;
    it’s easy to *understand* R = xp once you know
    that it’s going to be useful. it’s just far from obvious
    that it’s useful in the given context.

  6. ellie

    dont feel bad brutus! i left letter #4 (d) blank too… I was trying to visualize the notes in my head but something was blocking my view and i couldnt remember how to do it.

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