Question

Find the algebraic form g(x) of the function g whose graph is produced by the following transformations on thegraph of f(x) = ×: The graph of f is reflected vertically, expanded horizontally by a factor of 2, shifted right 6 units, and shifteddown 4 units. Include graphs off and g as a part of your answer.

Answer 1

Given the function f(x) = x

We will find the function g(x) whose graph is produced by the following transformations on the graph of f(x)

First, The graph of f is reflected vertically

So,

`\begin{gathered} f(x)\rightarrow f(-x) \\ g(x)=-x \end{gathered}`

Second, expanded horizontally by a factor of 2

So,

`\begin{gathered} f(-x)\rightarrow f(-2x) \\ g(x)=-2x \end{gathered}`

Finally, shifted right 6 units, and shifted down 4 units.

So,

`\begin{gathered} f(-2x)\rightarrow f(-2(x-6))-4 \\ g(x)=-2(x-6)-4 \end{gathered}`

Simplifying the function g(x):

`g(x)=-2x+8`

The graph of the function (f) and (g) will be as shown in the following figure: