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.

Front

What does the graph of an exponential function look like?

Back

The graph of an exponential function is a smooth curve that either increases or decreases rapidly, depending on the base 'b'. If b > 1, the graph rises steeply; if 0 < b < 1, it falls steeply.

Front

What is the base of an exponential function?

Back

The base of an exponential function is the constant 'b' in the function f(x) = a * b^x. It determines the rate of growth or decay.

Front

What is the y-intercept of an exponential function?

Back

The y-intercept of an exponential function f(x) = a * b^x is the point where the graph crosses the y-axis, which occurs at (0, a).

Front

How does changing the base 'b' affect the graph of an exponential function?

Back

Changing the base 'b' affects the steepness of the graph. A larger base results in a steeper increase, while a base between 0 and 1 results in a rapid decrease.

Front

What is the horizontal asymptote of an exponential function?

Back

The horizontal asymptote of an exponential function is the line that the graph approaches but never touches, typically y = 0 for functions of the form f(x) = a * b^x.

Front

What is exponential growth?

Back

Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to rapid increases over time, often modeled by f(t) = a * e^(kt).

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases at a rate proportional to its current value, often modeled by f(t) = a * e^(-kt).

Front

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

Back

An exponential function can be identified from a table of values if the ratio of consecutive outputs (y-values) is constant when the inputs (x-values) are increased by equal intervals.

Front

What is the difference between linear and exponential functions?

Back

Linear functions have a constant rate of change, resulting in a straight line graph, while exponential functions have a variable rate of change, resulting in a curve.