Question

Determine the transformations needed to get f(x)= 4+2x from f(x)=x

Answer 1

EXPLANATION:

Given;

We are given the equation of a graph which is;

$f(x)=x$

This is transformed to give us the equation;

$f(x)=4+2x$

Required;

We are required to determine the transformations needed to get

$\begin{gathered} f(x)=4+2x \\ from \\ f(x)=x \end{gathered}$

Solution;

Note that from the first graph, which is f(x) = x (or y = x), what we have is x equals y at every value of x. However, when we have y = 2x, then that means when x = 1, y = 2. That is, for every value of x, the value of y is doubled. The line is vertically stretched LEFT by 2 units.

Afterwards, the equation becomes;

$f(x)=4+2x$

This means you now move the line 4 units up along the y-axis.

Therefore,

ANSWER:

$\begin{gathered} Vertically\text{ }stretch\text{ }f(x)=x\text{ }left\text{ }by\text{ }2\text{ }units \\ \\ Transform\text{ }f(x)=x\text{ }up\text{ }by\text{ }4\text{ }units \end{gathered}$

We can now plot both graphs as follows:

Graph of

$f(x)=x$

Also, we would have;

Graph of

$f(x)=4+2x$

Observe that the graph after the transformation has now tilted to the left and has moved from the origin (where x = 0, y = 0) up to the point where y = 4 (that is, x = 0, y = 4)