Key features of 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 is the y-intercept of an exponential function?

Back

The y-intercept of an exponential function is the value of the function when x = 0, which is equal to 'a' in the function f(x) = a * b^x.

Front

Given the function y = 3^x, what is the y-intercept?

Back

The y-intercept is (0, 3), since f(0) = 3^0 = 1.

Front

What does the base of an exponential function determine?

Back

The base determines the rate of growth or decay of the function. If the base is greater than 1, the function grows; if the base is between 0 and 1, the function decays.

Front

Identify the y-intercept of the function f(x) = 13(0.27)^x.

Back

The y-intercept is 13, since f(0) = 13(0.27)^0 = 13.

Front

What is the general form of an exponential function?

Back

The general form is f(x) = a * b^x, where 'a' is the initial value and 'b' is the growth/decay factor.

Front

Given f(x) = 2(4)^x, what is the y-intercept?

Back

The y-intercept is 2, since f(0) = 2(4)^0 = 2.

Front

What is an asymptote in the context of exponential functions?

Back

An asymptote is a line that the graph of a function approaches but never touches. For exponential functions, the horizontal asymptote is usually the x-axis (y=0).

Front

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

Back

Changing the base affects the steepness of the graph. A larger base results in a steeper curve, while a smaller base (greater than 0 but less than 1) results in a flatter curve.

Front

What is the initial value in an exponential function?

Back

The initial value is the value of the function when x = 0, which is represented by 'a' in the function f(x) = a * b^x.