Showing posts with label functions. Show all posts
Showing posts with label functions. Show all posts
Monday, April 18, 2011
getting ahead of ourselves
from purplemath:
I'm a big fan of purplemath.This is actually something you will see again in calculus. I guess they're trying to "prep" you for upcoming courses when they give you exercises like this, but it's not like anybody remembers these by the time they get to calculus, so it's really a lot of work for no real purpose. However, this type of problem is quite popular, so you should expect to need to know how to do it.
- Given that f(x) = 3 x 2 + 2x, find [f(x + h) – f(x)] / h.
Thursday, January 17, 2008
Tuesday, January 15, 2008
question
This is a copy of an email I sent out to my local math list shortly before the last algebra test:
I found a nice group of “linear function” word problems today (answers included - pdf file).
Any thoughts?
I found a nice group of “linear function” word problems today (answers included - pdf file).
The kids in Math A are doing these problems. They aren’t classic Algebra 1 word problems, so if your child needs extra practice they’re not easy to come by.I'm curious about people's reaction to this shift in content. One of our regulars is skeptical; he sees this as a move to turn algebra into statistics. Another sees this as another instance of pushing advanced topics lower down in the curriculum. Functions used to be introduced in calculus; now kids see "function machines" in 3rd grade. (And, of course, both motivations could be involved - both and more.)
As I understand it, algebra 1 used to be focused on setting up and solving linear equations. The classic Algebra 1 word problems were number problems, consecutive integer problems, distance problems (2 trains leave a station), coin & age problems, & mixture & work problems.
Today algebra 1 tends to be focused on the idea of linear functions. That’s why our kids did all those “function machine” problems back at the Main Street School. In a linear function problem you are given a pair of “solutions” and asked to write an equation to model the situation. My favorite linear function word problem thus far is the Celsius – Fahrenheit conversion:
The graph of an equation to convert degrees Celsius, x, to degrees Fahrenheit, y, has a y-intercept of 32°. Given that water boils at 212°F and at 100°C, write the conversion equation.
To write the equation you use the two coordinated pairs you already know:
When Celsius is 0 degrees, Fahrenheit is 32
When Celsius is 100 degrees, Fahrenheit is 212
These two points are coordinated pairs on the graph of the function:
(0,32)
(100,212)
You derive the slope of the linear equation from these two points; then you plug in one of the coordinated pairs and derive the y-intercept; et voila.
y = 9/5 x + 32
Or:
F = 9/5C + 32
I've never been able to remember how to convert from Celsius to Fahrenheit, and knowing how to use the two known conversion points to produce the formula is great.
Any thoughts?
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