Unit 1: Exploring Rates of Change Flashcards
Domain
Set of all inputs of a function
Range
Set of all outputs of a function
Function
Describes the relationship between an independent and dependent variable
How can you tell a graph, table of values, or equation is a function?
Each input maps to EXACTLY ONE output
What does f(a) represent?
the y-value for some x-value=a
If the question states “find g(10)” what do you do?
plug 10 in for each x in the function and evaluate
If a<b, then f(a)<f(b).
Function is increasing on (a,b)
If a<b, then f(b)<f(a).
Function is decreasing on (a,b)
If the graph is concave up, what does that tell you about the rate of change?
Rate of change is increasing
If the graph is concave down, what does that tell you about the rate of change?
Rate of change is decreasing
Point of inflection
Where concavity changes and has the steepest slope
AROC stands for…
Average rate of change
How do you find average rate of change on the interval [a,b]?
Interpret the average rate of change…
“On average, the (y-variable context) changes by (AROC value) (y-unit) per unit of (x-variable context).”
In PreCalc, how do we “estimate” the instantaneous rate of change?
Find the average rate of change for a small interval around x=a.
