Functions
PICTURE: For this relation to be a function, the blank must be equal to this number.
What is -12?
PICTURE: The following table suggests that the limit at 5 is this number.
What is 8.5?
PICTURE: The limit of f(x) does not exist at this x-value.
What is 3?
The function f(x)=x/(x-2) is discontinuous at this point.
What is x=2?
The function G(x)=1/x is discontinuous at this point.
A graph isn't a function if it fails this test by having two or more points have the same x-value but different y-values.
What is the Vertical Line Test?
PICTURE: The table suggests the limit at x=2 is this.
What is DNE?
PICTURE: The limit of f(x) does not exist at these x-values.
What are 1 and 3?
For a function to be continuous at a certain point, these three quantities must all equal each other.
What are the left limit, the right limit, and the y-value?
PICTURE: This number is equal to the limit from the left of f(x) at x=3.
What is negative infinity?
We can represent functions in these four ways.
What are tables, graphs, words, and equations?
PICTURE: This number fills the blank in the table below.
What is 18.030201?
PICTURE: This number is the limit of the function shown as x goes to negative infinity.
What is 2?
DAILY DOUBLE
Draw a function that has exactly 3 points where it is discontinuous.
PICTURE: This number fills the blank in the table below.
What is 1.3333296?
DAILY DOUBLE
Come up with an example of a function using words and an example of a non-function using a graph. No credit for using any concept we've mentioned in class so far (coffee, best ___ in a city, etc...).
PICTURE: The table below suggests this about the limits of the function F.
What is the left limit at X=8 is 10?
See picture.
What are 1 and 2?
PICTURE: The function in the table below is continuous at this x-value.
What is 1?
The domain of the function k(x)=(x^2+8)/x includes all real numbers except for this number.
What is 0?
PICTURE: The relation F(x) is NOT a function because the input of 5 has these two outputs.
What are 23 and 15?
Using a table, compute the limit of F(x)=x^2+6x-10 as x goes to -2.
What is -18?
PICTURE: This is the limit of the graph as x approaches infinity.
What is DNE?
PICTURE: The function shown here is discontinuous at a because the left and right limits equal this number, while the y-value equals this other number.
What are 2 and 1?
This word describes how we're going to do on the exam.
What is WONDERFUL?