Exponential Functions Introduction

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 increases; if 0 < b < 1, the graph decreases.

Front

What is the y-intercept of an exponential function?

Back

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

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 the base of an exponential function affect its growth?

Back

The base 'b' determines the rate of growth: if b > 1, the function grows exponentially; if 0 < b < 1, the function decays exponentially.

Front

What is the domain of an exponential function?

Back

The domain of an exponential function is all real numbers, represented as (-∞, ∞).

Front

What is the range of an exponential function?

Back

The range of an exponential function is all positive real numbers, represented as (0, ∞).

Front

How do you identify an increasing exponential function?

Back

An exponential function is increasing if its base 'b' is greater than 1 (b > 1).

Front

How do you identify a decreasing exponential function?

Back

An exponential function is decreasing if its base 'b' is between 0 and 1 (0 < b < 1).

Front

What is the general form of an exponential function?

Back

The general form of an exponential function is f(x) = a * b^x, where 'a' is a constant and 'b' is the base.