Comparing Linear and Exponential Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has 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 f(x) = a(b^x), where a is a constant, b is the base (a positive real number), and x is the exponent.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the general form of an exponential equation?

Back

The general form of an exponential equation is f(x) = a(b^x), where a is a constant and b is the base.

Front

How do you identify a linear function from a table of values?

Back

A linear function will have a constant rate of change between the x-values and y-values.

Front

How do you identify an exponential function from a table of values?

Back

An exponential function will show a constant multiplicative rate of change between the y-values as x increases.

Front

What is the slope in a linear function?

Back

The slope (m) in a linear function represents the rate of change of y with respect to x.

Front

What does the y-intercept represent in a linear function?

Back

The y-intercept (b) is the value of y when x = 0, indicating where the line crosses the y-axis.

Front

What is the difference between linear and exponential growth?

Back

Linear growth increases by a constant amount, while exponential growth increases by a constant percentage.

Front

Can a linear function ever be exponential?

Back

No, a linear function cannot be exponential; they are distinct types of functions with different properties.