Function notation & rate of change

Front

What is function notation?

Back

Function notation is a way to represent a function using symbols, typically written as f(x), where 'f' is the name of the function and 'x' is the input variable.

Front

What does the domain of a function represent?

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

What is the average rate of change of a function?

Back

The average rate of change of a function over an interval [a, b] is calculated as (f(b) - f(a)) / (b - a).

Front

What does a constant rate of change indicate about a function?

Back

A constant rate of change indicates that the function is linear, meaning it has a constant slope.

Front

What is a non-linear function?

Back

A non-linear function is a function whose graph is not a straight line, indicating that the rate of change varies.

Front

How do you find the rate of change from a graph?

Back

To find the rate of change from a graph, select two points on the line, and use the formula (change in y) / (change in x).

Front

What is the significance of the slope in a linear function?

Back

The slope of a linear function represents the rate of change of the function, indicating how much y changes for a unit change in x.

Front

If f(x) = 3x + 2, what is f(1)?

Back

f(1) = 3(1) + 2 = 5.

Front

What does f(x) = y mean?

Back

f(x) = y means that for every input x, the function f produces an output y.