Exponential Graphs

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.

Front

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

Back

The graph of an exponential function increases rapidly for positive values of x and approaches the horizontal asymptote as x approaches negative infinity.

Front

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

Back

The horizontal asymptote is y = 0.

Front

What is the y-intercept of the function y = 2^x?

Back

The y-intercept is (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. A base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Front

What is the domain of an exponential function?

Back

The domain of an exponential function is all real numbers.

Front

What is the range of the function y = 2^x?

Back

The range is all real numbers greater than 0.

Front

How do you find the asymptote of the function y = 2^x - 3?

Back

The asymptote is found by setting the function equal to a constant. For y = 2^x - 3, the asymptote is y = -3.

Front

What is the effect of adding a constant to an exponential function, such as y = 2^x + 3?

Back

Adding a constant shifts the graph vertically. In this case, the graph shifts up by 3 units.

Front

What happens to the graph of y = 2^x as x approaches negative infinity?

Back

As x approaches negative infinity, y approaches the horizontal asymptote, which is y = 0.