1. ## linear functions

i did this sort of maths a lonnnnng time ago at school...and have since forgotten it! can you help me with this one?

A major pollutant produced by burning fossil fuels is sulfur dioxide (SO2). An investigation in Oslo, Norway, has shown that the number N of deaths per week is a linear function of the mean concentration C of SO2. Measured in
µg/m3. The empirical function is N = 94 + (0.031) C. The domain is {C|50 < C < 700}.

a) plot a graph of this function
b) calculate the range.

thanks so much!

2. Originally Posted by hollies_yardbirds_kinks
i did this sort of maths a lonnnnng time ago at school...and have since forgotten it! can you help me with this one?

A major pollutant produced by burning fossil fuels is sulfur dioxide (SO2). An investigation in Oslo, Norway, has shown that the number N of deaths per week is a linear function of the mean concentration C of SO2. Measured in
µg/m3. The empirical function is N = 94 + (0.031) C. The domain is {C|50 < C < 700}.

a) plot a graph of this function
b) calculate the range.

thanks so much!
This is a graph of the function on the particular domain $50:

Note here, that the "origin" in this case starts at the y value of 100. Mathematica squished this together....

The range of this line over the particular domain is determined by substituting the endpoints of the domain into the equation for the line.

I leave it for you to show that the range is $95.55.

I hope this makes sense!

--Chris

3. Originally Posted by hollies_yardbirds_kinks
i did this sort of maths a lonnnnng time ago at school...and have since forgotten it! can you help me with this one?

A major pollutant produced by burning fossil fuels is sulfur dioxide (SO2). An investigation in Oslo, Norway, has shown that the number N of deaths per week is a linear function of the mean concentration C of SO2. Measured in
µg/m3. The empirical function is N = 94 + (0.031) C. The domain is {C|50 < C < 700}.

a) plot a graph of this function
b) calculate the range.

thanks so much!
The given function is
N = 94 +(0.031)C

That means The N is dependent on the C. So the range is about possible values of N depending on the the values of C in the domain.

Graph that function using the horizontal axis representing C, and the vertical axis reprenting N. As is usual, the range is in those vertical corrdinates.

To graph a linear function, you just need two points on the line.

When C = 0,
N = 94 +(0.031)(0) = 94
So, point (0,94) --------------one poit

When C = 700,
N = 94 +(0.031)(700) = 94 +21.7 = 115.7
So, point (700,115.7) --------another point

Plot those two points on the same (C,N) set of axes, run a straight line through them, and that is the graph of the given function.

For the range,
since the domain of C is from 50 to 700 only, then get the value of N at C=50 and at C=700 to find the range,

When c = 50,
N = 94 +(0.031)(50) = 95.55

When C = 700, we found that N = 115.70

Therefore, the range is from 95.55 to 115.70 --------answer.

4. thank you so much! this really explains it well.