Rates of change, polynomial end behavior, zeros, rational function asymptotes, holes and transformations.
41 cards · basic cards · AI-written, checked twice. Edit anything.
- Average rate of change formula
Show answer
(f(b) - f(a)) / (b - a), or change in y over change in x- Difference quotient
Show answer
(f(x + h) - f(x)) / h- Secant line versus tangent line
Show answer
Secant connects two distinct points on a curve; tangent touches at one point and represents instantaneous rate of change- Instantaneous rate of change
Show answer
The rate of change at a single point, found as the limit of average rate as the interval approaches zero- How to compute rate of change from two table values
Show answer
Calculate (y2 - y1) / (x2 - x1)- What determines the end behavior of a polynomial?
Show answer
The degree and the sign of the leading coefficient- Odd degree polynomial, positive leading coefficient
Show answer
Graph enters from lower left and exits to upper right- Odd degree polynomial, negative leading coefficient
Show answer
Graph enters from upper left and exits to lower right- Even degree polynomial, positive leading coefficient
Show answer
Graph enters from upper left and exits to upper right- Even degree polynomial, negative leading coefficient
Show answer
Graph enters from lower left and exits to lower right- How degree affects polynomial end behavior
Show answer
Odd degree: opposite directions at each end; even degree: same direction at both ends- How leading coefficient sign affects polynomial end behavior
Show answer
Positive leading coefficient: graph rises to the right; negative: graph falls to the right- Define a zero or root of a polynomial
Show answer
An x-value where the polynomial equals zero; appears as an x-intercept on the graph- Relationship between a zero c and a factor
Show answer
If c is a zero, then (x - c) is a factor of the polynomial- State the Factor Theorem
Show answer
A polynomial p(x) has (x - c) as a factor if and only if p(c) = 0
FlashKeepers