3.1.3 - 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 graph up 3 units?

Back

Translating a graph up 3 units means shifting every point on the graph vertically upwards by 3 units.

Front

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

Back

Reflecting a graph over the x-axis means flipping the graph over the x-axis, changing the sign of the y-coordinates of all points.

Front

What does it mean to reflect a graph over the y-axis?

Back

Reflecting a graph over the y-axis means flipping the graph over the y-axis, changing the sign of the x-coordinates of all points.

Front

What is the effect of the transformation 2^(-x) on the graph of 2^x?

Back

The transformation 2^(-x) reflects the graph of 2^x over the y-axis.

Front

What is the effect of the transformation -2^x on the graph of 2^x?

Back

The transformation -2^x reflects the graph of 2^x over the x-axis and also flips it vertically.

Front

What does the transformation 2^x - 3 do to the graph of 2^x?

Back

The transformation 2^x - 3 translates the graph of 2^x downwards by 3 units.

Front

What is a vertical translation in graph transformations?

Back

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

Front

What is a horizontal translation in graph transformations?

Back

A horizontal translation moves the graph left or right without changing its shape.

Front

How does changing the base of an exponential function affect its graph?

Back

Changing the base of an exponential function affects the rate of growth or decay; a larger base results in a steeper graph.