Exponential Functions flashcard

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 a positive real number, and x is the exponent.

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as x increases, the value of f(x) also increases.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing if, as x increases, the value of f(x) decreases.

Front

What is the y-intercept of a function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, which occurs when x=0.

Front

What is an asymptote?

Back

An asymptote is a line that a graph approaches but never touches or crosses.

Front

How do you find the y-intercept of an exponential function?

Back

To find the y-intercept of an exponential function, substitute x=0 into the function and solve for f(0).

Front

What is the general shape of the graph of an increasing exponential function?

Back

The graph of an increasing exponential function rises steeply as x increases.

Front

What is the general shape of the graph of a decreasing exponential function?

Back

The graph of a decreasing exponential function falls steeply as x increases.

Front

How do you solve an exponential equation like 8^(3x+3) = 8^6?

Back

Set the exponents equal to each other: 3x + 3 = 6, then solve for x.

Front

What is the base in an exponential function?

Back

The base is the constant b in the function f(x) = a * b^x, which determines the rate of growth or decay.