Important Terms
When you use a model to predict an output value for an input value that is outside the input data range- you are using ____________.
extrapolation
When a function does not have a value and a limit, we say the function value or limit ______ _____ _____.
does not exist (DNE)
Linear Function
f(x) = ax + b
no concavity
nearly constant first differences
Break-even point
point where revenue = cost
When do you use MATH SOLVER? When do you use Y1 (vars)?
MATH SOLVER- when you are given an output and need to find an input
Y-vars- when you are given an input and need to find an ouput
A rule that assigns exactly one output value (y) to each input unit (x) is called a ________.
function
If you see an open circle at a point, does a function have a value there?
No, but an open circle does not mean that there cannot be a limit.
Exponential function
f(x) = ab^x
one concavity
percent change is nearly constant
horizontal asymptote at y=0 (x-axis)
Total cost
fixed costs + variable costs
When you are given a domain in a question, what do you need to adjust on your calculator?
WINDOW
When a function is increasing/decreasing most rapidly, it is at a _________ ____.
inflection point
Look at the graph of example 2 on page 16 in your lecture guide. What is the limit of f(x) as 2 goes to 2?
limf(x) as x goes to 2 = approximately 40
Logarithmic function
f(x) = a + bln(x)
one concavity
restrictive domain (0, infinity)
gradual increase or decrease
vertical asymptote at x=0 (y-axis)
Profit
revenue - cost
When do we use ZoomStat? When do we use ZoomFit?
ZoomStat is when we get a list of data and use it to see the scatterplot
ZoomFit is if we a given a function that we need to see on a graph
The _______ ________ ____ over a single unit input interval is equal to (b-1) 100%.
constant percentage change
Look at the graph on page 15 in your lecture guide. Is the function continuous at x=1? Why or why not?
No
f(1) = 3
limf(x) as x goes to 1 = -2
3 does not equal -2
Logistic function
f(x) = L / (1 + ae^-bx)
two concavities
"S" shape
2 limiting values at y=L and y=0 (horizontal asymptotes)
has inflection point
Average cost
total cost / # items produced
How do you find an inverse of data in your calculator?
Switch your L1 and L2
If a function is one-to-one, then it has an _____ ______.
inverse function
What are the three conditions for a function to be continuous at input c?
1. f(c) exists
2. limf(x) as x goes to c exists
3. limf(x) as x goes to c = f(c)
Cubic function
f(x) = ax^3 + bx^2 + cx + d
has inflection point
can show relative max or min
2 ends in opposite directions
Revenue
(selling price / units) (# units sold)
If they give you a checkpoint for a question, what does it mean you have to do?
Put the function in your calculator and check it at the checkpoint to make sure you put it in right!