Polynomial Power
The maximum number of real zeros a 5th-degree polynomial can have.
What is 5?
This feature occurs on a graph when a factor in the denominator of a rational function evaluates to zero and is not canceled out by a matching factor in the numerator.
What is a vertical asymptote?
The mathematical constant that serves as the base of the natural logarithm.
What is e?
The horizontal asymptote of the parent function f(x) = 2x
What is y = 0?
The period of the parent sine function y = sin(x).
What is 2pi?
If a polynomial has a zero with a multiplicity of 2, the graph does this at the x-axis.
What is touches (or bounces off / is tangent to)?
This graphical feature occurs at x = 2 in the function
f(x) = (x-2)/(x2-4).
What is a hole?
The evaluated integer result of log2(8) + log2(2).
What is 4?
If a population doubles every 5 years, this is the growth factor per 5-year cycle.
What is 2?
The amplitude of the function f(x) = -4cos(2x) + 1
What is 4?
The end behavior of [f(x) = -3x4 + 2x - 1] as x -> infinity
What is -Infinity?
The equation of the horizontal asymptote for
f(x) = (4x2 - 1)/(2x2 + 3).
What is y = 2?
The fully expanded form of ln(x2y).
What is 2ln(x) + ln(y)?
The algebraic expression for the value of an investment of $100 compounded continuously at a rate of 5% for t years.
What is A = 100e0.05t?
The rectangular equation for the polar equation r = 5.
What is x2 + y2 = 25?
A polynomial with roots at x = 1, x = -2, and x = 3 can be written in this factored form.
What is f(x) = (x-1)(x+2)(x-3)?
A rational function has this type of asymptote when the degree of the numerator is exactly one greater than the degree of the denominator.
What is a slant asymptote?
The domain of the function f(x) = log10(x - 5).
What is x > 5 (or (5, Infinity)?
The inverse function of f(x) = 10x.
What is f-1(x) = log(x) (or log10(x))?
The rectangular x-coordinate of the polar point (4, (pi/6))
What is 2sqrt(3)?
If 3 + 2i is a root of a polynomial with real coefficients, this complex number must also be a root.
What is 3 - 2i?
The number of vertical asymptotes for the function
f(x) = x/(x2+1).
What is zero/none?
The exact solution to the equation ln(x) + ln(x-1) = ln(2)
What is x = 2? (Note: x = -1 is extraneous!)
The term for the amount of time it takes for an exponentially decaying quantity to reach exactly 50% of its initial amount.
What is the half-life?
The maximum distance from the pole for the polar curve
r = 2 - 4cos(theta)
What is 6?