Linear vs Exponential

Front

What is the definition of a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is the definition of an exponential function?

Back

An exponential function is a mathematical 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

How can you identify a linear function from its graph?

Back

A linear function can be identified by its straight-line graph, which has a constant slope and does not curve.

Front

How can you identify an exponential function from its graph?

Back

An exponential function can be identified by its curve that increases or decreases rapidly, showing a constant percentage change rather than a constant amount.

Front

What is the slope of a linear function?

Back

The slope of a linear function is the ratio of the change in y to the change in x (rise over run), indicating how steep the line is.

Front

What does it mean for a function to add a constant to y-values as x-values change?

Back

It indicates that the function is linear, as it shows a constant rate of change in y for each unit change in x.

Front

What does it mean for a function to multiply y-values as x-values change?

Back

It indicates that the function is exponential, as it shows a multiplicative rate of change in y for each unit change in x.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.

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 and b is the base.

Front

What is the y-intercept in a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, represented by the value of b in the equation f(x) = mx + b.