Learn It Part 2

We must remember quite a lot of rules when determining how a function is transformed.

Consider the parent exponential function f of x.

The graph of an exponential growth function with horizontal asymptote y equals zero and passes through the point (0, 1). It is labeled f of x.

This function f of x is transformed to form the function g of x.

The graph of the exponential growth function has been reflected in the x axis and has translated up three units. It is now labeled g of x.

How was the function f of x transformed?

The first characteristic is to notice the function f of x has been flipped upside down. This means that the function has been multiplied by a negative one (negative1).

g sub one of x equals negative one times f of x

The graph of the exponential growth function f of x reflected in the x axis.

Note also how the function f of x is translated three units up. This means the function has the value of three added to it.

g(x)=negative1f(x)+3g of x equals negative one times f of x plus three

The graph of the exponential growth function f of x reflected in the x axis and then translated up three units to form the resulting function g of x.

Therefore, the translation of the function f of x to form the function g of x is noted as g of x equals negative one times f of x plus three.

Both the function f of x and the translated function g of x are graphed.

Calculator Tip

graphing calculator

When you are unsure of how the value of k will transform a function, graph various functions in your graphing calculator to test out the effects of k.

Visit the following website for instruction on graphing functions in the graphing calculator:

Mathbits: Graphing Functions in the Graphing Calculator Opens a new window