Functions and Systems of Equations Flashcards
A function is a rule that assigns ______ ______ output for each possible _______.
exactly one
input
The _______ is a function of the ______.
output
input
The _______ depends on the ______.
output
input
A graph of an equation is a function if it passes the ______ ______ test.
vertical line
We know that a table of values is a function if none of the _____ values are repeated.
x, input, or independent variable
We know that a list of coordinates is a function if none of the _____ values are repeated.
x, input, or independent variable
The independent variable is represented by which axis on a graph?
x
The dependent variable is represented by which axis on a graph?
y
The input to a function is the _______ variable.
independent
The output of a function is the ______ variable.
dependent
Is this the graph a function?
No. It does not pass the vertical line test.
Is this the graph a function?
No. It does not pass the vertical line test.
Is this the graph of a function?
Yes. It passes the vertical line test.
Is this the graph of a function?
Yes. It passes the vertical line test.
Is this the graph a function?
No. It does not pass the vertical line test.
A system of equations has only one solution if the _______ of each equation is ________.
slope
different
A system of equations has ______ ________ when the _______ of each equation is the same but the y-intercepts are different.
no solution
slope
A system of equations infinite solutions if each equation has the ______ ______ and ________.
same slope
y-intercepts
The graph of a system of equations that has one solution will show that the two lines do what?
cross or intersect
The graph of a system of equations that has no solution will show that the two lines do what?
The two lines will be parallel.
The graph of a system of equations that has infinite solutions will show that the two lines do what?
The two lines will be exaclty on top of each other.
In other words, they are the same line.
