# Variation and Graphs

Direct-variation function a function with a formula of the form y = kx^n, with k not equalling 0 and n > 0.
constant of variation y = kx^n, where k is a nonzero constant (called constant of variation)
Steps to solving variation functions 1. Write an eqution that describes the variation.
2. Find the constant of variation.
3. Rewrite the variation function using the constant of variation.
4. Evaluate the function for the desired value of the independent variable
inverse-variation function a function with a formula of the form y = k/x^n, when k does not equal 0 and n > 0.
The Fundamental Theorem of Variation a. If y varies directly as x^n (That is, y = kx^n.), and x is multiplied by c, then y is multiplied by c^n.
b. If y varies inversely as x^n (That is, y = k/x^n.), and x is multiplied by a nonzero constant c, then y is divided by c^n.
Are slope and rate of change the same thing? Yes
What is the graph of equation y = kx? A line
Does the graph of equation y = kx^2 lie on a strait line? No, you can verify by finding slope between points
What type of symmetry does a parabola have? reflection-symmetry and the y-axis is the line of symmetry
what is the domain and range of a parabola that opens up? domain: all real numbers
range: nonnegative real numbers
what is the domain and range of a parabola that opens down? domain: all real numbers
range: nonpositive real numbers
What form is the graph y = k/x? A hyperbola
In what quadrants is the hyperbola in for the equation y = k/x when k > 0? I and III
What quadrants is the hyperbola in for the equation y = k/x when k < 0? II and IV
graph of y =k/x^2 is called what type of function? inverse-square curve
In what quadrants is the equation Y =k/x^2 for k>0 in and what is the domain and range? I and II. domain=(x:x does not equal 0) range=(y: y>0)
In what quadrants is the equation y=k/x^2 for k<0 and what is the domain and range? III and IV. domain=(x:X does not equal 0) range=(y:Y<0)
what is the simplest equation of combined variation? y=kx/z
What is the simplest equation of joint variation? y=kxz