APPLIED ALGEBRA EXAM 9 QUESTIONS
WITH DETAILED VERIFIED ANSWERS
Equation
A mathematical statement that two things are equal; it consists of two expressions, one on each
side of an equals sign.
Data
A collection of facts, which might be numbers, words, measurements, observations or simply
descriptions.
Variable
Something that can vary, often used in equations, and usually represented by a letter (e.g., t for
time, n for number, c for color).
Quantitative Variable
A changing variable that is measured on a number scale; a variable with a numeric value.
Qualitative Variable or Categorical Variable
A variable that is not numeric; it describes data that fits into categories.
Independent Variable
A variable that, as it changes, affects another variable (called the dependent variable). For
example, as gas (the independent variable) is pumped into a car's tank, the cost of the purchase
(the dependent variable) rises. The input of a function.
Dependent Variable
A variable that is changed by another variable (called the independent variable). For example,
when purchasing gas, the cost (dependent variable) rises as more gas (the independent variable)
is pumped into the car's tank. Dependent variables are usually drawn on the y-axis of a graph.
The output of a function.
Input
, A quantitative variable that is chosen to find a solution, or output, of a function.
Output
A quantitative variable that is produced by a function when an input is chosen.
Function
A mathematical relationship between two variables where every input is matched with exactly
one output value.
y = f(x)
Format: Dependent Variable (Independent Variable)
This is not a multiplication equation; it is read as "the value of f at x" or "for a given input of x,
what is the function's output?"
Inverse Function
A function that undoes, or reverses, the action of another function (e.g., using multiplication to
check division).
The inverse of f(x) is written f^-1(x) and read "f inverse of x."
Graph
A diagram showing the relationship between variable quantities on two axes drawn at right
angles.
x,y
Independent Variable, Dependent Variable
Origin
On a graph, the starting point where both x and y are equal to zero, and the x-axis and the y-axis
intersect.
Interval
A range of numbers that include all the real numbers between its endpoints.
WITH DETAILED VERIFIED ANSWERS
Equation
A mathematical statement that two things are equal; it consists of two expressions, one on each
side of an equals sign.
Data
A collection of facts, which might be numbers, words, measurements, observations or simply
descriptions.
Variable
Something that can vary, often used in equations, and usually represented by a letter (e.g., t for
time, n for number, c for color).
Quantitative Variable
A changing variable that is measured on a number scale; a variable with a numeric value.
Qualitative Variable or Categorical Variable
A variable that is not numeric; it describes data that fits into categories.
Independent Variable
A variable that, as it changes, affects another variable (called the dependent variable). For
example, as gas (the independent variable) is pumped into a car's tank, the cost of the purchase
(the dependent variable) rises. The input of a function.
Dependent Variable
A variable that is changed by another variable (called the independent variable). For example,
when purchasing gas, the cost (dependent variable) rises as more gas (the independent variable)
is pumped into the car's tank. Dependent variables are usually drawn on the y-axis of a graph.
The output of a function.
Input
, A quantitative variable that is chosen to find a solution, or output, of a function.
Output
A quantitative variable that is produced by a function when an input is chosen.
Function
A mathematical relationship between two variables where every input is matched with exactly
one output value.
y = f(x)
Format: Dependent Variable (Independent Variable)
This is not a multiplication equation; it is read as "the value of f at x" or "for a given input of x,
what is the function's output?"
Inverse Function
A function that undoes, or reverses, the action of another function (e.g., using multiplication to
check division).
The inverse of f(x) is written f^-1(x) and read "f inverse of x."
Graph
A diagram showing the relationship between variable quantities on two axes drawn at right
angles.
x,y
Independent Variable, Dependent Variable
Origin
On a graph, the starting point where both x and y are equal to zero, and the x-axis and the y-axis
intersect.
Interval
A range of numbers that include all the real numbers between its endpoints.
