The Basics
This is how you determine if a graph is a function.
What is the Vertical Line Test?
Graph #4 has an absolute minimum at this coordinate.
What is (-1,2)?
The intervals at which graph #3 is increasing and decreasing.
What is increasing (-infinity, -2) and decreasing (-2, infinity)?
The calculator buttons to press to calculate extrema of the graph of a function.
What is 2nd, Trace (calc)?
The average rate of change over [-1,0] of f(x)=2x2 - 1.
What is -2?
The number of x-intercepts of graph #3.
What are (-3,0) and (-1,0)?
Graph #2 has a relative minimum at this coordinate.
What is (2,-7)?
The intervals at which graph #2 is increasing and decreasing.
What is increasing (-infinity, 0) and (2, infinity) and decreasing (0,2)?
The local and absolute minimum of f(x)= -x2 + 2x - 3.
What is no local and no absolute minimum?
The average rate of change over [0,1/2] of f(x)=2x2 + x + 2.
What is 2?
The y-intercept of graph #1.
What is (0,-4)?
What is a maximum?
What is decreasing (-infinity, 0) and (2, infinity) and increasing (0,2)?
The local minimum of f(x)= -x4 + 4x2 - 2.
What is (0,-2)?
The average rate of change over [-1,1] of f(x)=2x2 + 2.
What is 0?
What is even?
Of the 6 graphs, these are the only one(s) with no absolute minimum AND no absolute maximum.
What are graphs #2, 5, and 6?
The intervals at which graph #1 is increasing and decreasing.
What is increasing (-infinity, -1) and (0,1) and decreasing (-1,0) and (1, infinity)?
The absolute maximum of f(x)= -x4 + 4x2 - 2.
What are (-1.4,2) and (1.4,2)?
The average rate of change over [-1,0] of f(x)= -2x2 + x - 1.
What is 3?
The domain and range of graph #4.
What is domain (-infinity, infinity) and range [2, infinity)?
This may be considered when determining absolute extrema but NOT local exrema.
What are endpoints?
The intervals at which graph #6 is either increasing or decreasing.
What is decreasing (-infinity, 4), (4, infinity)
The intervals on which f(x)= x4 - 4x2 + 5 is increasing and decreasing.
What is increasing (-1.4,0) and (1.4, infinity) and decreasing (-infinity, -1.4) and (0,1.4)?
The average rate of change is this of the secant line of a function.
What is slope?