Exponential Transformations & Characteristics

Front

What is an asymptote in the context of exponential functions?

Back

An asymptote is a line that a graph approaches but never touches. For exponential functions, it often represents a horizontal line that the function approaches as x approaches positive or negative infinity.

Front

What is the effect of subtracting a constant from an exponential function, such as f(x) = 3^x - 4?

Back

Subtracting a constant shifts the graph vertically. In this case, the graph of f(x) = 3^x - 4 is shifted 4 units down from the basic function g(x) = 3^x.

Front

What is the horizontal asymptote of the function f(x) = 3^x - 4?

Back

The horizontal asymptote is y = -4.

Front

What is the right end behavior of the function f(x) = 3^x?

Back

As x approaches positive infinity, f(x) approaches positive infinity.

Front

What happens to the value of f(x) as x approaches negative infinity for the function f(x) = 3^x?

Back

As x approaches negative infinity, f(x) approaches 0.

Front

What is the general form of an exponential function?

Back

The general form of an exponential function is f(x) = a * b^(x - h) + k, where (h, k) is the translation of the graph.

Front

How does the base of an exponential function affect its growth?

Back

A larger base results in faster growth. For example, f(x) = 2^x grows slower than f(x) = 3^x.

Front

What is the vertical asymptote of the function f(x) = 2^(x) + 3?

Back

The vertical asymptote does not exist for this function; it has a horizontal asymptote at y = 3.

Front

What is the transformation of the function f(x) = 2^(x - 2)?

Back

The function is shifted 2 units to the right.

Front

What is the effect of multiplying an exponential function by a negative number, such as f(x) = -2^x?

Back

Multiplying by a negative number reflects the graph across the x-axis.