Exponential Transformations Flashcard

Front

What is a horizontal translation in exponential functions?

Back

A horizontal translation shifts the graph of the function left or right along the x-axis. For example, a function of the form f(x) = a^(x - h) translates the graph h units to the right.

Tags

CCSS.HSF-IF.C.7E

Front

What is a vertical translation in exponential functions?

Back

A vertical translation shifts the graph of the function up or down along the y-axis. For example, f(x) = a^x + k translates the graph k units up if k > 0 and down if k < 0.

Tags

CCSS.HSF-IF.C.7E

Front

What is an asymptote in the context of exponential functions?

Back

An asymptote is a line that the graph of a function approaches but never touches. For exponential functions, the horizontal asymptote is typically y = 0.

Tags

CCSS.HSF-IF.C.7E

Front

What is the difference between exponential growth and decay?

Back

Exponential growth occurs when the base of the exponential function is greater than 1 (e.g., f(x) = a^x where a > 1). Exponential decay occurs when the base is between 0 and 1 (e.g., f(x) = a^x where 0 < a < 1).

Tags

CCSS.HSF-IF.C.8B

Front

What does it mean to reflect a function over the x-axis?

Back

Reflecting a function over the x-axis means that for every point (x, y) on the graph, there is a corresponding point (x, -y). This changes the sign of the output values.

Tags

CCSS.HSF.BF.B.3

Front

How do you identify a vertical translation in an exponential function?

Back

A vertical translation can be identified by a constant added or subtracted from the function, such as f(x) = a^x + k, where k indicates the vertical shift.

Tags

CCSS.HSF.BF.B.3

Front

What is the effect of a negative coefficient in front of an exponential function?

Back

A negative coefficient reflects the graph over the x-axis, changing the direction of growth or decay.

Tags

CCSS.HSF-IF.C.7E

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 point, a is the vertical stretch or compression, and b is the base.

Tags

CCSS.HSF.LE.A.2

Front

What does the base of an exponential function determine?

Back

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

Tags

CCSS.HSF-IF.C.8B

Front

What is the significance of the point (0, 1) in exponential functions?

Back

The point (0, 1) is significant because it represents the value of the function when x = 0 for any exponential function of the form f(x) = a^x, where a > 0.

Tags

CCSS.HSF-IF.C.7E