Linear and Exponential Functions Review

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is an exponential function?

Back

An exponential function is a function of the form y = ab^x, where a is a constant, b is the base (a positive real number), and x is the exponent.

Front

How can you identify a linear relationship from a set of data?

Back

A linear relationship can be identified if the change in y is constant for a constant change in x, resulting in a straight line when graphed.

Front

How can you identify an exponential relationship from a set of data?

Back

An exponential relationship can be identified if the ratio of the change in y to the change in x is constant, resulting in a curve that increases or decreases rapidly when graphed.

Front

What does it mean for a function to be neither linear nor exponential?

Back

A function is neither linear nor exponential if it does not fit the characteristics of either type, such as quadratic functions or other non-linear relationships.

Front

Convert the expression 2^3 into exponential form.

Back

2^3 is already in exponential form.

Front

Convert the expression 16 into radical form.

Back

16 can be expressed as 4^2, which is the radical form of the square root of 16.

Front

What is the slope of a linear function?

Back

The slope of a linear function is the ratio of the rise (change in y) to the run (change in x), often represented as 'm' in the equation y = mx + b.

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, represented by 'b' in the equation y = mx + b.

Front

What is the base in an exponential function?

Back

The base in an exponential function is the constant 'b' in the expression y = ab^x, which determines the rate of growth or decay.