Direct/Inverse Variation
Determine an equation for y varies directly as the square of x
What is y=kx2?
y=(x^2-4x+3)/(4x^2-4)
has this horizontal asymptote.
What is y=1/4?
y=((x-2)(x+1))/((x+1)(x-2))
has this vertical asymptote(s).
What is x=-2?
y=((x-2)(x+1))/((x+2)(x-2))
has these x-intercept(s).
What is x=-1?
Simplify the expression
y=(x^2-1)/(3x^2-3)
What is 1/3?
Determine an equation for y varies directly as x and inversely as z
What is
y=(kx)/z
y=3/(x+5)
has this horizontal asymptote. x-2
What is y=0?
y=((x-4)(x+1))/((x-4)(x-1))
has this x-value for a hole.
What is x=4?
y=(4x(x-4))/((x+2)(x-4))
has these x-intercept(s).
What is x=0?
Factor 2x2 + 2x
What is 2x(x+1)?
The equation for this type of variation is z=kxy.
What is joint variation?
y=(x^3-6x^2+4x-7)/(6x^2+4x-7)
has this horizontal asymptote. 6-x^2+2x
What is f(x) has no horizontal asymptote?
y=(3x^2-12)/(x^2+3x+2)
has this vertical asymptote(s).
What is x=-1?
y=(3x^2-12)/(x^2+3x+2)
has this y-intercept.
What is y=-6?
Multiply
(((x-5)^2)/(x^2+3x+2))xx(((x+1)(x+2))/(x-5))
What is (x-5)?
This type of variation has a graph in the shape of a rational function.
What is an inverse variation?
Horizontal asymptotes do this.
What is define end behavior.
y=(x^2)/(x^2-1)
has this/these vertical asymptote(s).
What is x=1 and x=-1?
y=(x^2)/(3x^2-3)
has this y-intercept.
What is y=0?
Divide
((x^2+6x+5)/(5x^2))//((10x)/(x^2-25))
(2(x+1))/(x(x-5))
This type of variation shown has this constant of variation: y = kx , with points (-3, -15) , (25, 75)
What is direct variation with a constant equal to 5?
This is type of asymptote may be crossed, this type may not be touched at all .
What is a graph will not cross a vertical asymptotes, but may cross a horizontal asymptote?
y=(4(x-5)(x+1))/(2(x-5))
has this point as a hole in its graph.
What is (4, 12)?
A graph can have more than one of this type of intercept.
What is x-intercept?
Divide
What is x+4