Linear vs Exponential Functions

Front

What is the difference between linear and exponential functions?

Back

Linear functions have a constant rate of change and can be represented by a straight line (y = mx + b). Exponential functions have a variable rate of change and can be represented by a curve (y = a * b^x).

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 y = a * b^x, where a is a constant, b is the base (growth factor), and x is the exponent.

Front

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

Back

A linear function will show a constant difference in the y-values for equal increments in the x-values.

Front

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

Back

An exponential function will show a constant ratio of the y-values for equal increments in the x-values.

Front

What does the slope of a linear function represent?

Back

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

Front

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

Back

The y-intercept represents the value of y when x is 0, indicating where the line crosses the y-axis.

Front

What does the base in an exponential function represent?

Back

The base represents the growth factor; if b > 1, the function is increasing, and if 0 < b < 1, the function is decreasing.

Front

How do you graph a linear function?

Back

To graph a linear function, plot the y-intercept on the y-axis and use the slope to find another point, then draw a straight line through the points.

Front

How do you graph an exponential function?

Back

To graph an exponential function, plot the initial value (when x=0) and use the growth factor to find additional points, then draw a smooth curve.