11/22 Algebra: Exponential Functions Graph Characteristics

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form y = a * b^x, where a is a constant, b is the base (a positive real number), and x is the exponent. It shows rapid growth or decay.

Front

What is the general form of an exponential function?

Back

The general form of an exponential function is y = a * b^x, where a is the initial value, b is the growth (b > 1) or decay (0 < b < 1) factor, and x is the exponent.

Front

What is the y-intercept of an exponential function?

Back

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

Front

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

Back

The y-intercept is (0, 3).

Front

What does the constant 'a' represent in the exponential function y = a * b^x?

Back

The constant 'a' represents the initial value or the y-intercept of the function.

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 typically y = 0.

Front

What is the horizontal asymptote of the function y = 2^x?

Back

The horizontal asymptote is y = 0.

Front

How do you determine the average rate of change of a function?

Back

The average rate of change of a function f from x = a to x = b is calculated as (f(b) - f(a)) / (b - a).

Front

If N = 3(2^m), what does the constant 3 represent?

Back

The constant 3 represents the initial number of rabbits Gabriela started with.

Front

What is the significance of the base 'b' in an exponential function?

Back

The base 'b' determines the rate of growth or decay. If b > 1, the function represents exponential growth; if 0 < b < 1, it represents exponential decay.