Glossary
Concave Down
A characteristic of a function's graph where it curves downward, resembling a frown, indicating that its rate of change is decreasing.
Example:
The graph of f(x) = -x² is concave down over its entire domain, as its slope becomes less positive or more negative.
Concave Up
A characteristic of a function's graph where it curves upward, resembling a bowl, indicating that its rate of change is increasing.
Example:
The graph of f(x) = x² is concave up over its entire domain, showing its slope is continuously getting steeper.
Decreasing Function
A function where, as the input values increase, the corresponding output values decrease.
Example:
The function f(x) = -x is a decreasing function because as x gets larger, f(x) gets smaller.
Dependent Variable
The output variable in a function, whose value depends on the input or independent variable.
Example:
If the amount of gas in your car's tank decreases as you drive, the amount of gas is the dependent variable.
Domain
The set of all possible input values for which a function is defined.
Example:
For the function f(x) = 1/x, the domain includes all real numbers except x=0, because division by zero is undefined.
Function
A relationship where each input from the domain has exactly one output in the range.
Example:
The cost of a pizza is a function of its size; for each size, there's only one price.
Function Rule
The specific method or formula that describes how inputs are transformed into outputs for a given function.
Example:
The function rule f(x) = 2x + 1 tells you to double the input and add one to get the output.
Increasing Function
A function where, as the input values increase, the corresponding output values also increase.
Example:
The function f(x) = x³ is an increasing function over its entire domain, as larger x-values always lead to larger y-values.
Independent Variable
The input variable in a function, whose value is chosen or controlled and affects the output.
Example:
In an experiment measuring plant growth over time, time is the independent variable because its value is set by the experimenter.
Range
The set of all possible output values that a function can produce.
Example:
For the function f(x) = x², the range is all non-negative real numbers, as squaring any real number results in a value greater than or equal to zero.
Zeroes
The input values for which a function's output is zero, representing the points where the graph intersects the x-axis.
Example:
For the function f(x) = x - 5, the zero is x = 5, because f(5) = 0.