### 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 .

**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 …)

February 1, 2009 at 12:32 am

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?

February 1, 2009 at 8:30 am

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!! :-)

February 2, 2009 at 12:39 pm

@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!

February 2, 2009 at 5:08 pm

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.

February 2, 2009 at 5:53 pm

for anybody

notin the class:usually the main problem with problems

like my number

4is the first step:we require that the student

knowthat “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.

February 3, 2009 at 2:41 am

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.