Algebra ETA Q2: Functions (with ROC and DV)

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

How can you determine if a relation is a function?

Back

A relation is a function if every input value corresponds to exactly one output value. This can be checked using the vertical line test on a graph.

Front

What does ROC stand for in the context of functions?

Back

ROC stands for Rate of Change, which measures how a quantity changes in relation to another quantity.

Front

What is a constant rate of change?

Back

A constant rate of change means that the output of a function changes by the same amount for each unit increase in the input.

Front

What is an example of a function with a constant rate of change?

Back

An example is the function f(x) = 2x, where the rate of change is always 2.

Front

What is an example of a function that is not a function?

Back

An example is the relation {(1, 2), (1, 3)}, which is not a function because the input 1 corresponds to two different outputs.

Front

What is the difference between a function and a non-function?

Back

A function has one output for each input, while a non-function can have multiple outputs for a single input.

Front

What is an ordered pair in the context of functions?

Back

An ordered pair is a pair of numbers (x, y) that represents a point on the graph of a function, where x is the input and y is the output.