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 does the base of an exponential function determine?

Back

The base determines the rate of growth or decay. If the base is greater than 1, the function represents exponential growth; if the base is between 0 and 1, it represents exponential decay.

Front

What is the transformation in y = 2^(x-3)?

Back

The graph of the function is shifted to the right by 3 units.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches positive or negative infinity.

Front

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

Back

The horizontal asymptote is y = 2.

Front

How do you determine if a function is exponential growth or decay?

Back

If the base of the exponential function is greater than 1, it is exponential growth. If the base is between 0 and 1, it is exponential decay.

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 with a positive base?

Back

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

Front

What is the y-intercept of the function y = 3 * 2^x?

Back

The y-intercept is the point where x = 0, which gives y = 3 * 2^0 = 3.

Front

What is the effect of a vertical stretch on an exponential function?

Back

A vertical stretch occurs when the coefficient 'a' in the function f(x) = a * b^x is greater than 1, making the graph steeper.