2.1 Functions Flashcards
a rule that assigns each element in one set to a unique element in a second set
function
being the only one of its kind
unique
a set of ordered pairs in which no two ordered pairs have the same first coordinate and different second coordinates
function
“is a function of” means
is determined by
there is more than one value of the output that corresponds to the same input
not a function
the input or first coordinate
independent variable
the output or second coordinate
dependent variable
a set of ordered pairs
relation
Name the ways you can represent a relation
1) verbal description
2) graph
3) formula
4) equation
5) table
How do you determine if a relation is a function if you have a list of ordered pairs?
check to see if any of the x’s repeat. If so, do they have the same y-coordinate? If the y-coordinates are the same for the repeated x-coordinate, then the relation is a function. If you have different y- coordinates for the same x-coordinate, then the relation is not a function.
How do you determine if a relation is a function if you are given a graph?
Draw a vertical line on the graph. If the line passes the vertical line test, the relation is a function. If not, the relation is not a function.
How do you determine if a relation is a function if you are given an equation?
Solve for y. Did you take an even root to solve for the value of y? If so, there would be a plus or minus in front of the root giving two outputs for the same input. Therefore, the equation is not a function. If you did not take the even root of both sides of the equation to solve for y, then it would automatically be a function for “MOST” items. There are exceptions that are not taught in this course.
What is the vertical line test?
a graph is the graph of a function if and only if there is no vertical line that crosses the graph more than once.
the set of all first coordinates of the ordered pairs
domain
the set of all second coordinates of the ordered pairs
range
How do you find the domain of any equation?
Look for places the function is undefined. Exclude these values.
Which functions could have breaks in their domain?
1) functions that have variables in the denominator
2) functions with even roots
3) piece-wise defined functions (some)
4) logarithms
5) some trigonometric functions
6) circles
How do you find the domain of a set of ordered pairs?
List all the x-values from least to greatest. Do not repeat values.
How do you find the range of a set of ordered pairs?
List all the y-values from least to greatest. Do not repeat values.
How do you find the domain of a function that contains an even root?
Set the radicand greater than or equal to zero and solve. Write the answer in interval notation.
How do you find the domain of a function that contains a variable in the denominator?
Set the denominator not equal to zero and solve. Write the answer in interval notation.
How do you find the domain of a function that contains an even root in the denominator?
Set the denominator > 0 and solve. Write the answer in interval notation.
Which functions have domains of “all real numbers”?
All lines except vertical.
Polynomial functions
Exponential functions
Absolute value functions.
Odd root functions that are not in a denominator.
Greatest Integer functions
provides a rule for finding the second coordinate or output
function notation
the change in y-coordinates divided by the change in x-coordinates
average rate of change
Formula for the difference quotient
a function relating two variables in a geometric figure (formula)
construct
