VGChartz teaches me mathzz: Precalculus edition

[pearljammer]

Soriku said:

pearljammer said:

Soriku said:

1. The number of horsepower H required to overcome wind drag on an automobile is approximated by the model:

H(x) = 0.002x^2 0.005x - 0.029, 10 < x < 100

where x is the speed of the car in miles per hour.

Rewrite the function so that x represents speed in kilometers per hour [Find H(x/1.6).] Describe the transformation applied to the graph of the function.

h(x *1/b) will casue a horizontal dilation with a scale factor of 1/1.6

It will scale up (widen because |1.6| >1

That answers the second part of your question.

The first section of your question, you just simply replace x with x/1.6 in your initial function.

If I plug in 1.6 to my function 0.002(1.6)^2 0.005(1.6) - 0.029 (btw I forgot to add a after 0.002x in my OP) I get like -0.0178. Am I doing it right? What do I do with 10 < x < 100?

Edit: lol you teach math for a living? Well sorry it's just getting out there at this point. :/ I used to like math...not anymore.

Good try, but you're not looking for a solution. You're re-writing the equation so that it measures in kilometres.

What the question is, is simply presenting you with a basic transformation. The complicated equation is only a distraction. When you have a transformation of form f(x) -> f(1/b *x) you have a dilation or a change of scale - widen or shorten horizontally.

Try a more simple example on your calculator to illustrate the point:  Y1 = x^2    and    Y2= (x/1.6)^2  See when b>1 it widens.

See how that same transformation works on a simple function? The same behaviour will occur with the transformation on your question. You should probably have some notes on transformations - check them over too!

I'm unsure if your teacher wants anything done with the 10 < x < 100 part.

Yeah, I teach math. Typically junior high, though. Haven't had much opportunity with high school maths yet besides general/basic courses.