Rate of change and finding domain and range

Front

What is the rate of change?

Back

The rate of change is a measure of how a quantity changes in relation to another quantity, often expressed as the ratio of the change in the dependent variable to the change in the independent variable.

Front

How do you calculate the average rate of change?

Back

The average rate of change is calculated using the formula: (Y2 - Y1) / (X2 - X1).

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

If a function is defined as f(x) = 2x + 3, what is its domain?

Back

The domain is all real numbers, as there are no restrictions on x.

Front

If a function is defined as f(x) = x^2, what is its range?

Back

The range is all real numbers greater than or equal to 0, since x^2 cannot be negative.

Front

What does it mean if a function is linear?

Back

A linear function is a function that can be graphically represented in the Cartesian plane as a straight line, characterized by a constant rate of change.

Front

What is a vertical line test?

Back

The vertical line test is a method used to determine if a curve is a function. If any vertical line intersects the curve more than once, it is not a function.

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 dependent variable with respect to the independent variable.

Front

What is an example of a function with a restricted domain?

Back

An example is f(x) = 1/x, which is defined for all real numbers except x = 0.