Studied by 3 people
Average Rate of Change
Measures how much the function value changes over an interval relative to the change in x.
Increasing Function
A function where the values rise as x increases, indicating a positive slope/rate of change.
Decreasing Function
A function where the values fall as x increases, indicating a negative slope/rate of change.
Constant Function
A function that neither increases nor decreases over an interval.
Concave Up
The graph of the function looks like a smile, indicating that the slope is increasing.
Concave Down
The graph of the function looks like a frown, indicating that the slope is decreasing.
Linear Function
A function with a constant rate of change, represented by the equation y = mx + b.
Quadratic Function
A function where rates of change form a linear pattern, represented by the equation f(x) = ax^2 + bx + c.
Polynomial Function
A function of degree n, where nth order rates of change are constant when x values are evenly spaced.
Local Maximum
A point where a function transitions from increasing to decreasing.
Local Minimum
A point where a function transitions from decreasing to increasing.
Point of Inflection
The point at which concavity changes; the graph switches from curving upwards to curving downwards.
Complex Roots
If a complex number z = a + bi is a root of a polynomial function with real coefficients, its complex conjugate z = a - bi must also be a root.
Polynomial End Behavior
Determined by the degree and the sign of the leading coefficient.
Rational Functions Zeroes
Zeroes of R are zeroes of P that are not also zeroes of Q.
Hole in the Graph
Occurs when both P and Q equal zero at x = c; indicates that the function is undefined.
Vertical Asymptote
Occurs at x-values where Q(x) = 0 while P(x) is non-zero.
End Behavior of Rational Functions
Indicates whether the function approaches 0, infinity, or negative infinity as x approaches positive/negative infinity.
Binomial Expansion
Can be found using box multiplication or Pascal’s Triangle.
Base Logarithmic Function
A logarithmic function assumed to be base 10 when no subscript is provided.
Natural Logarithms
Equal to regular logarithms with e as the subscript.
Standard Position in Trigonometry
The vertex is at the origin with one ray of the angle on the positive x-axis.
Arc Length Formula
Calculation method for the length of an arc on a circle.
Unit Circle
A circle with a radius of one used in trigonometry to define sine, cosine, and tangent.
Trigonometric Functions Equation
y = Asin(B(x+c)) + D where A is amplitude, period is 2π/B, phase shift is C, and the midline is y = D.
Modeling with Semi-log Plot
When the vertical axis is logarithmically scaled and the graph appears linear, it indicates an exponential function.
Residual Plot Interpretation
A pattern in a residual plot means the model is inappropriate, while no pattern indicates appropriateness.
