Exponential Function 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 does it mean to translate a function to the right?

Back

Translating a function to the right means shifting the graph of the function horizontally to the right by a certain number of units.

Front

What does it mean to translate a function up?

Back

Translating a function up means shifting the graph of the function vertically upwards by a certain number of units.

Front

What is a reflection in the context of functions?

Back

A reflection is a transformation that flips the graph of a function over a specified line, such as the x-axis or y-axis.

Front

What is the parent function of an exponential function?

Back

The parent function of an exponential function is f(x) = b^x, where b is a positive constant.

Front

How does a negative coefficient affect an exponential function?

Back

A negative coefficient reflects the graph of the exponential function across the x-axis.

Front

What is the effect of a horizontal translation on the function f(x) = b^x?

Back

A horizontal translation shifts the graph left or right, changing the input value x to (x - h) or (x + h), where h is the number of units.

Front

What is the range of an exponential function f(x) = a * b^x?

Back

The range of an exponential function is (0, ∞) if a > 0, and (-∞, 0) if a < 0.

Front

What does it mean to reflect a function over the line y=0?

Back

Reflecting a function over the line y=0 means flipping the graph of the function across the x-axis.

Front

What is the transformation of f(x) = 2^x - 3?

Back

The transformation is a vertical translation down 3 units.