3.1.3 - Exponential Function Transformations

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.

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

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.

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.

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

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

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

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

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

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