Graphing 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 does it mean for an exponential function to be increasing?

Back

An exponential function is increasing if the base 'b' is greater than 1, meaning as 'x' increases, the value of f(x) also increases.

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

What is an asymptote in the context of exponential functions?

Back

An asymptote is a horizontal line that the graph of an exponential function approaches but never touches, typically the line y = 0 for exponential growth.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base 'b' is greater than 1, while exponential decay occurs when the base 'b' is between 0 and 1.

Front

How do you identify the y-intercept in the function f(x) = 50(1.4)^x?

Back

The y-intercept is found by evaluating f(0), which gives f(0) = 50(1.4)^0 = 50.

Front

What is the growth factor in an exponential function?

Back

The growth factor is the base 'b' in the function f(x) = a(b)^x, which determines how much the function increases for each unit increase in 'x'.

Front

What is the general form of an exponential decay function?

Back

The general form of an exponential decay function is f(x) = a(b)^x, where 0 < b < 1.

Front

How can you determine if a function is exponential decay from its equation?

Back

If the base 'b' in the function f(x) = a(b)^x is between 0 and 1, the function represents exponential decay.

Front

What is the initial value in the function f(x) = 13(0.27)^x?

Back

The initial value is the y-intercept, which is 13, found by evaluating f(0) = 13(0.27)^0.