Exponential Graphs 1st period only

Front

What is a transformation in the context of exponential graphs?

Back

A transformation refers to a change in the position or shape of the graph, such as shifting it left, right, up, or down.

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 horizontal asymptote for the function f(x) = 3(2)^(x-4) + 5?

Back

The horizontal asymptote is found by identifying the constant term added to the exponential function, which is y = 5.

Front

What does the equation y = 4(1/2)^x represent in terms of graph behavior?

Back

This equation represents an exponential decay function, where the graph approaches the horizontal asymptote as x increases.

Front

What is the effect of a leftward transformation on the graph of an exponential function?

Back

A leftward transformation shifts the graph to the left by the specified number of units.

Front

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

Back

The base determines the rate of growth or decay; a base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Front

How can you identify the vertical asymptote of an exponential function?

Back

Exponential functions do not have vertical asymptotes; they have horizontal asymptotes.

Front

What is the general form of an exponential function?

Back

The general form is y = a(b)^x, where 'a' is a constant, 'b' is the base, and 'x' is the exponent.

Front

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

Back

As x approaches negative infinity, y approaches 0, indicating the horizontal asymptote.

Front

What is the transformation of the graph y = 2^x when it is written as y = 2^(x-3)?

Back

This represents a rightward transformation of 3 units.