Show:
Direct/Inverse Variation
Horizontal Asymptotes
Vertical Asymptotes & Holes
Intercepts
Rational Functions
100
Determine an equation for y varies directly as the square of x
What is y=kx^2?
100
x^2-3x f(x)= ------------ has this horizontal asymptote. 5-4x^2
What is y=1/4?
100
(x-2)(x+1) f(x)= -------------- has this vertical asymptote(s). (x+2)(x-2)
What is x=-2?
100
(x-2)(x+1) f(x)= -------------- has these x-intercept(s). (x+2)(x-2)
What is x=-1?
100
x^2-1 Simplify the expression ----------- 3x^2-3
What is 1/3?
200
Determine an equation for y varies directly as x and inversely as z
What is y=kx/z?
200
3 f(x)= ------ has this horizontal asymptote. x-2
What is y=0?
200
(x-4)(x+1) f(x)= -------------- has this x-value for a hole. (x+2)(x-4)
What is x=4?
200
4x(x-4) f(x)= -------------- has these x-intercept(s). (x+2)(x-4)
What is x=0?
200
6x^2 x^2-1 Multiply -------- & ---------- x-1 3x
What is 2x(x+1)?
300
The equation for this type of variation is z=kxy.
What is joint variation?
300
x^3+3x^2-12 f(x)= ----------------- has this horizontal asymptote. 6-x^2+2x
What is f(x) has no horizontal asymptote?
300
3x^2-12 f(x)= -------------- has this vertical asymptote(s). x^2+3x+2
What is x=-1?
300
3x^2-12 f(x)= -------------- has this y-intercept. x^2+3x+2
What is y=-6?
300
(x-5)^2 x^2+3x+2 Multiply ----------- & -------------- x+1 (x+2)(x-5)
What is (x-5)?
400
This type of variation has a graph in the shape of a hyperbola.
What is an inverse variation?
400
A graph will not cross a horizontal asymptote here.
What is for the large x-values near positive and negative infinity?
400
x^2 f(x)= ----------- has this vertical asymptote(s). 3x^2-3
What is x=1 and x=-1?
400
x^2 f(x)= ----------- has this y-intercept. 3x^2-3
What is y=0?
400
4x^2y 10xy Divide ---------- & --------- 2x+2 x^2-1
x(x-1) What is --------- ? 5
500
This type of variation is shown in the table and has this constant of variation: x y 3 15 8 40 10 50
What is direct variation with a constant equal to 5?
500
This is the difference between horizontal and vertical asymptotes (besides the direction).
What is a graph will not cross a vertical asymptotes, but may cross a horizontal asymptote?
500
4(x-5)(x+1) f(x)= --------------- has this point as a hole in its graph. 2(x-5)
What is (4, 12)?
500
A graph can have more than one of this type of intercept.
What is x-intercept?
500
3x+6 6x Divide ----------- & -------------- 3x^2-12 x^2+2x-8
x(x-6) What is --------- ? 5