Comparing Functions TEST

Front

What is 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. It shows rapid growth or decay.

Front

What is a linear function?

Back

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

Front

What does the y-intercept represent in a function?

Back

The y-intercept is the point where the graph of a function crosses the y-axis. It is the value of the function when x = 0.

Front

How do you determine the rate of change in a linear function?

Back

The rate of change in a linear function is determined by the slope (m) in the equation f(x) = mx + b. It represents how much y changes for a unit change in x.

Front

What is the difference between exponential growth and linear growth?

Back

Exponential growth increases at a rate proportional to its current value, leading to faster increases over time, while linear growth increases by a constant amount.

Front

What is the slope of a linear function?

Back

The slope of a linear function is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as x increases, the value of f(x) also increases. This is true for both linear and exponential functions.

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax^2 + bx + c, where 'a', 'b', and 'c' are constants.

Front

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

Back

A linear function will have a constant rate of change between the x-values and corresponding y-values in a table.

Front

What is the significance of the base in an exponential function?

Back

The base in an exponential function determines the growth rate. A base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.