Exponential Graphs

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 general shape of an exponential graph?

Back

Exponential graphs typically rise or fall rapidly, depending on whether the base 'b' is greater than 1 (increasing) or between 0 and 1 (decreasing).

Front

What is the y-intercept of an exponential function?

Back

The y-intercept of an exponential function f(x) = a * b^x is the point (0, a).

Front

What does the horizontal asymptote of an exponential function represent?

Back

The horizontal asymptote of an exponential function represents the value that the function approaches as x approaches positive or negative infinity.

Front

How do you find the y-intercept of the function y = 4^x + 2?

Back

To find the y-intercept, substitute x = 0: y = 4^0 + 2 = 1 + 2 = 3, so the y-intercept is (0, 3).

Front

What is the horizontal asymptote of the function y = 2^x - 3?

Back

The horizontal asymptote is y = -3, as the function approaches this value as x approaches negative infinity.

Front

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

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 an example of a decreasing exponential function?

Back

An example of a decreasing exponential function is f(x) = 5 * (0.5)^x.

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 an exponential function of the form f(x) = a * b^x + k?

Back

The range is (k, ∞) if a > 0, and (-∞, k) if a < 0.