Graphing Simple Exponential Functions

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 characterizes exponential growth?

Back

Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to a rapid increase over time.

Front

What characterizes exponential decay?

Back

Exponential decay occurs when the decrease of a value is proportional to its current value, leading to a rapid decrease over time.

Front

Identify the general form of an exponential growth function.

Back

The general form is f(x) = a * b^x, where b > 1.

Front

Identify the general form of an exponential decay function.

Back

The general form is f(x) = a * b^x, where 0 < b < 1.

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 value of f(0), which equals 'a'.

Front

How do you determine if a function is exponential growth or decay from its equation?

Back

If the base 'b' is greater than 1, it is exponential growth. If 'b' is between 0 and 1, it is exponential decay.

Front

What is the effect of a negative coefficient in an exponential function?

Back

A negative coefficient reflects the graph across the x-axis, indicating a decay if the base is greater than 1.

Front

What does the term 'asymptote' refer to in exponential functions?

Back

An asymptote is a line that the graph approaches but never touches, typically the x-axis (y=0) for exponential functions.

Front

How can you identify exponential growth on a graph?

Back

Exponential growth is identified by a curve that rises steeply to the right.