Exponential Functions: Graphs, Asymptotes and Transformations

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 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 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 - 3?

Back

y = -3.

Front

What does a vertical translation of an exponential function do?

Back

A vertical translation shifts the graph up or down without changing its shape.

Front

What is the effect of a horizontal translation on the graph of an exponential function?

Back

A horizontal translation shifts the graph left or right along the x-axis.

Front

What does a reflection across the x-axis do to the graph of an exponential function?

Back

A reflection across the x-axis inverts the graph, making all positive values negative.

Front

What is the transformation of the function f(x) = 2^x + 3 compared to g(x) = 2^x?

Back

The transformation is a vertical translation 3 units up.

Front

How do 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 equation of the horizontal asymptote for the function y = 3^x - 4?

Back

y = -4.