College Algebra

[Shuiessen]

Hey I have homework due soon and I was stuck on these couple problems, could someone please help


Elevation (ft) Snowfall (in)
2000 4
3000 6
4000 9
5000 12

1. Let X represent the elevation in feet and a(x) represent the amount of snowfall in inches. Determine a(4000).

2. Write a sentence explaining the meaning of a(5000)=12


3.Name the input and output, and write the name of each function. Y=g(x)

 

[Denis]

Is this REALLY "college" algebra?
What d'heck is "college" these days?

 

[Shuiessen]

It's Intermediate Algebra, basically for people who suck at it, do you think you could help?

 

[mmm4444bot]

These two exercises both deal with the meaning of function notation (which you have forgotten).

Function notation is another way to write y. Function notation gives more information than simply writing the symbol y.



EG: Consider the following relationship between numbers x and y.

y = x^2 + 16

This is a function. The number y depends upon the value of the number x.

The variable x is called the independent variable (AKA: "the function input").

The variable y is called the dependent variable (AKA: "the function output").

With function notation, we use different symbolism for the output y; we write f(x), instead.

y = f(x)

The letter "f" is the name of the function. (It's standard to use letters f, g, and h, but I could have named this function using any letter; it's just a name.)

With function notation, the parentheses enclose the input.

f(x) = x^2 + 16

If we input the value x = 1 into this function f, we get the output y = 17.

Using function notation, we write the output like this: f(1)

In other words, the notation f(1) means y when x is 1, and it's value is 17.

f(1) = 17

If we input x = 4, the function f outputs y = 32

f(4) = 32



Your first exercise defines a function by providing a table of inputs and their corresponding outputs. (We do not have a formula, for generating the y-values in this function; we have only the table to work with.)

Instead of the letter "f", they named this function "a".

This function inputs an elevation and outputs the snowfall depth at that elevation.

x = the input

a(x) = the output

So we have y = a(x)

From the first input/output pair in the table, we can write the xy pair using function notation:

a(2000) = 4

Here we see the input is 2000 and the output is 4.

This tells us that the snowfall is four inches (y) at an elevation of 2,000 feet (x).

Function notation allows us to state a lot of information without having to write much.



EG:

There is no entry in the given table for elevations above 5,000 feet, but let's pretend that:

a(15000) = 43

This statement tells us that you'll find 43 inches of snow after climbing to an elevation of 15,000 feet.

Succinct, huh ?



Can you now find the value of a(4000) ?

It's right there, in the table.

a(4000) represents the output when 4000 is the input.

Can you now explain the meaning of a(5000) = 12 ?

What is the name of the function here: Y = g(x) ?

What symbol represents the input ? The output ?

Good luck with your remedial math studies.

(I hope that you're not taking any math courses on-line. You need face-to-face instruction.)