Linear vs Exponential Functions

Front

What is a linear function?

Back

A linear function is a function that creates a straight line when graphed. 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 in which an independent variable is in the exponent. It has the form y = ab^x, where a is a constant, b is the base, and x is the exponent.

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

Back

A linear function will have a constant rate of change, meaning the difference between consecutive y-values is the same for equal changes in x.

Front

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

Back

An exponential function will have a constant ratio of change, meaning the ratio of consecutive y-values is the same for equal changes in x.

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What does the graph of a linear function look like?

Back

The graph of a linear function is a straight line that can slope upwards or downwards.

Front

What does the graph of an exponential function look like?

Back

The graph of an exponential function shows rapid growth or decay, appearing as a curve that increases or decreases sharply.

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 is the y-intercept in a linear function?

Back

The y-intercept (b) in a linear function is the value of y when x is 0.

Front

What happens to the value of an exponential function as x increases?

Back

As x increases, the value of an exponential function can grow very quickly (if b > 1) or decrease rapidly (if 0 < b < 1).

Front

What is a common real-world example of a linear function?

Back

A common example is calculating the total cost of items at a fixed price, such as y = 5x, where x is the number of items.