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# Chapter 2

### Variation and graphs

A DIRECT-VARIATION FUNCTION is a function with a formula of the form y=kx^n with k does not equal 0 and n>0 EX: r=5c
A car needs 25 ft to stop after braking at 20 mph. braking distance d is directly porportional to the square of the speed s. What distance is needed to stop this car braking at 60 mph? 1) Find equation; d=ks^2 2) Determine constant; 25=k*(20)^2; k= 1/16 3) Substiute k; d= 1/16*s^2 4) Evaluate; d= 1/16*60^2; d=225
An INVERSE-VARIATION FUNCTION is af unction with a formula of the form y=k/x^n with k does not equal 0 and n>0 EX: t=36/s
THE FUNDAMENTAL THEOREM OF VARIATION a) If y varies directly as x^n (y=kx^n) and x is muliplied by c, then y is multiplied by c^n. b) If y varies inversely as x^n (y=k/x^n)and x is multiplied by a nonzero constant c, then y is divided by c^n.
The SLOPE of the line thorugh two pints (x1, y1) and (x2,y2) equals (y2-y1)/(x2-x1) EX: (10,2) (15,3); (3-2)/(15-10)= 1/5
CONVERSE OF THE FUNDAMENTAL THEOREM OF VARIATION a. If multplying every x-value of a function by c results in multiplying the corresponding y-value by c^n then y=kx^n b. If multiplying every x-value of a function by c resluts in dividing the corresponding y-value by c^n then y=k/x^n
COMBINED VARIATION is when direct and inverse variations occur together EX: y=kx/z
JOINT VARIATION is when one qantity varies directly as the product of two or more independent variable but not inversely as any variable EX: y=kxz
When y=kx what will the graph look like? a line that cross origin; d and r = all real numbers; when k>0 the line goes up from right to left; when k,o the line goes down right to left
When y=kx^2 what will the grpah look lke? parabola; hits origin; d always set of all real numbers; when k>0 parabola opens up and r= non negative real numbers; when k<0 parabol opens down and r=negative real numbers
When y= k/x what will the graph look like? hyperbola; doesnt pass trhough origin;d and r= set of all nonzero real numbers; when k>0 in 1st and 3rd quadrant; when k<0 in 2nd and 4th quadrant
When y- k/x^2 what will the graph look like? inverse-square curve; d= set of all nonzero real numbers; when k>0 in 1st and 2nd quadrants and r= y>0; when k<0 in 3rd and 4th quadrants and r= y<0
Created by: jessries0139