Question

Describe how to transform the graph of f(x)=x^2 to obtain the graph of the related function g(x). Then draw the graph of g(x).G(x)=f(x+1)

Answer 1

Let f(x) is a function and a function g(x) is given by,

`g(x)=f(x+C)`

Here, if C is positive, then the graph of g(x) is the graph of f(x) shiftedC units to the left.

If C is negative, then the graph of g(x) is the graph of f(x) shifted C units to the right.

Given:

`\begin{gathered} f(x)=x^2 \\ g(x)=f(x+1) \end{gathered}`

Then, g(x) can be expressed as, ,

`g(x)=(x+1)^2`

From the explanation above, g(x) is the graph of f(x) shifted 1 unit to the left.

Now, the graph of g(x) can be drawn as: