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# MAT 211 Lecture 1 Notes- Section 15.1 MAT 211

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This 3 page Class Notes was uploaded by Brigette Maggio on Thursday January 14, 2016. The Class Notes belongs to MAT 211 at Arizona State University taught by Dr. Mohacsy in Fall 2015. Since its upload, it has received 24 views. For similar materials see Math for Business Analysis in Math at Arizona State University.

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Date Created: 01/14/16

MAT 211Lecture #1 Section 15.1Functions with Several Variables M/W/ F 99:50 AM Coor 199 Office Hours: M/W/F 1:15 3:00 PM ECA 209 R(x)= Revenue function in terms of number of items x P(x)= Profit function in terms of number of items x C(x)= Cost function in terms of number of items x P(x)= R(x) C(x) most of functions depend on more than one variable function with a single variable has a rule that assigns a unique output for every input x> f > y=f (x) Ex.: f(x)= e + 1 or f(x)= 3x +2x+5 2 y= 3x +2x+5 Linear Functions: y= mx+b m= slope (rate of change) b= vertical intercept Ex.: f(x)= 3x+2 y= 3x+2 Ex.: A car salesperson’s yearly salary is $30,000. He/ she makes $500 per car sale. x= number of cars he/ she sells s(x)= yearly salary in terms of x s(x)= 30,000+ 500x A real valued function f of x,y,z, etc. is a rule that assigns a unique output value for each sequence of input values x,y,z,etc. Ex.: Function with 3 variables w= f(x,y,z)= x+2y+z Find: f(0,0,0)= 0 Find: f(1,2,3)= 8 x=1, y=2, & z=3 Find: f(a,3,4)= a+10 x=a, y=3, & z=4 Find: f(x+h,3,1)= (x+h) +7 x=x+h, y=3, & z=1 Ex.: Function with 2 variables z= f(x,y)= x + y 4x+1 Find: f(0,0)=1 Find: f(1,1)= 1 1 4(1)+1 1+14+1= 1 2 2 Find: f(a+h, 0)= (a+h) +0 4(a+h)+1= (a+h) 4(a+h)+1 Linear functions with 2 variables: z= f(x,y) = 2x3y+5 +2 is the slope in the x direction 3 is the slope in the y direction The rate of change with respect to x when the y value is fixed= 2. The rate of change with respect to y when the x value is fixed= 3. A Linear Function with 2 variables: z=f (x,y)= ax+by+c where a is the slope (rate of change in the x direction) where b is the slope (rate of change in the y direction) A Linear Function with 3 variables: w= f(x,y,z)= ax+by+cz+d

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