Exponential vs Linear Functions!

Front

What is an exponential function?

Back

A function where the variable is in the exponent, typically in the form f(x) = a * b^x, where b > 0 and b ≠ 1.

Front

What is a linear function?

Back

A function that graphs to a straight line, typically in the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is the growth factor in an exponential function?

Back

The constant factor by which the function's value increases for each unit increase in x.

Front

What is the decay factor in an exponential function?

Back

The constant factor by which the function's value decreases for each unit increase in x.

Front

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

Back

If the difference between consecutive y-values is constant as x increases by 1, it is linear.

Front

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

Back

If the ratio of consecutive y-values is constant as x increases by 1, it is exponential.

Front

What does it mean for a function to have a constant rate of change?

Back

The change in y for each unit change in x is the same, characteristic of linear functions.

Front

What is the general form of an exponential growth function?

Back

f(x) = a * b^x, where a > 0 and b > 1.

Front

What is the general form of an exponential decay function?

Back

f(x) = a * b^x, where a > 0 and 0 < b < 1.

Front

What is the slope of a linear function?

Back

The rate of change of the function, represented by 'm' in the equation f(x) = mx + b.