Linear Functions vs. Exponential Functions

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. It represents growth or decay.

Front

How can you identify a linear function from its equation?

Back

A linear function will have no exponents on the variable other than 1. For example, y = 2x + 3 is linear.

Front

How can you identify an exponential function from its equation?

Back

An exponential function will have the variable in the exponent. For example, y = 3^x is exponential.

Front

What is the growth factor in an exponential function?

Back

The growth factor is the base of the exponential function, which determines how much the function grows or decays. For example, in y = 2(3^x), the growth factor is 3.

Front

What does the slope represent in a linear function?

Back

The slope represents the rate of change of the function. It indicates how much y changes for a unit change in x.

Front

What is the y-intercept in a linear function?

Back

The y-intercept is the value of y when x = 0. It is the point where the line crosses the y-axis.

Front

What is the difference between linear growth and exponential growth?

Back

Linear growth increases by a constant amount, while exponential growth increases by a constant percentage, leading to faster growth over time.

Front

If a function doubles every time x increases by 1, what type of function is it?

Back

It is an exponential function.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.