Consider f(x) = 2(x b)2 + 2. a State the coordinates of the vertex. b Find the axes intercepts. c The graph of function g is obtained by translating the graph of f vertically through b units. For what values of b will the graph of g: i have exactly one x-intercept ii have no x-intercepts iii pass through the origin?
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.: (x)= e+ 1 or f(x)= +2x+5 +2x+5 = 3x 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) +