Analyzing Functions
The output f(x) of a function decreases as the value of x increases.
What is decreasing behavior?
A function f(x) is shifted left or right on the x-axis.
What is a horizontal translation?
A function of the form a*xn
What is a monomial function?
The root of a function appears multiple times
f(x) = (x-c)(x-c)
What is a repeating root or multiplicity?
Solving for f(x) = 0 gives you this.
What is the x - intercept(s)?
f(x) + k
What is a vertical translation?
Monomials that always have one discontinuity.
What is a negative exponent?
The behavior of a graph "bounces" off of the x-axis at the root.
What is an even multiplicity?
The point at which a graph changes from decreasing to increasing behavior.
What is a minimum?
-f(x)
What is an x-axis reflection?
Monomials that often have a restricted range.
What is a rational exponent?
A polynomial f(x) has a factor (x-c) if and only if f(c) = 0
What is the factor theorem?
For every x in the domain of f, f(-x) = f(x).
What is the test for even functions?
f(a*x)
What is a horizontal dilation?
A value of x seems like a solution, but evaluating f(x) results in a nonsensical statement.
What is an extraneous solution.
If a polynomial f(x) is divided by (x-c), the remainder is r = f(c).
What is the remainder theorem?
f(c) is undefined
OR
lim x->c from the left is not equal to lim x->c from the right
OR
lim x->c is not equal to f(c)
What is a discontinuity?
What is a vertical dilation and a y-axis reflection?
What is xn/p where n and p are positive and odd?
f(x) = (x-i)(x+i)
What are complex conjugate roots?