Linear vs Exponential Tables, Graphs, Equations

Front

What is the difference between linear and exponential functions?

Back

Linear functions have a constant rate of change and can be represented by the equation y = mx + b, where m is the slope. Exponential functions have a variable rate of change and can be represented by the equation y = ab^x, where a is the initial value and b is the growth factor.

Front

How can you identify an exponential function from its equation?

Back

An exponential function can be identified by the presence of a variable in the exponent, such as in the equation g(x) = 250 * 3^x.

Front

What does the term 'y-intercept' mean in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0. In the equation y = 3x + 5, the y-intercept is 5.

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 does the base in an exponential function represent?

Back

The base in an exponential function represents the growth factor. For example, in the function y = 2 * 3^x, the base is 3, indicating that the function grows by a factor of 3 for each unit increase in x.

Front

How do you determine if a function is linear or exponential from a table of values?

Back

If the differences between consecutive y-values are constant, the function is linear. If the ratios of consecutive y-values are constant, the function is exponential.

Front

What is the significance of the coefficient in front of the exponential term?

Back

The coefficient in front of the exponential term represents the initial value or starting amount of the function. For example, in g(x) = 250 * 3^x, the initial value is 250.

Front

What is an example of a linear function?

Back

An example of a linear function is y = 2x + 3.

Front

What is an example of an exponential function?

Back

An example of an exponential function is y = 5 * 2^x.

Front

How can you graph a linear function?

Back

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