Question

1A. Graph the function f(x) = x^2 for the domain (-2, 2). The graph of g is obtained from the graph of f with a transformation 2 units up. What is the equation of g(x)?

Answer 1

ANSWER and EXPLANATION

We want to first graph the function given for the domain (-2, 2).

That domain given means that x is between - 2 and 2.

So let us pick the points:

x = -2, -1, 0, 1 and 2

Therefore, we will find f(x) for those values:

`\begin{gathered} f(-2)=(-2)^2\text{ = 4} \\ f(-1)=(-1)^2\text{ = 1} \\ f(0)=(0)^2\text{ = 0} \\ f(1)=(1)^2\text{ = 1} \\ f(2)=(2)^2\text{ = 4} \end{gathered}`

Now, let us graph it.

That is the graph of f(x) = x^2 in the domain (-2, 2)

Now, we have that g is obtained from f by translating it 2 units up.

Let us represent that in the graph by simply moving the graph of f(x) upwards with 2 units:

The red graph represents the graph of g(x).

For the equation of g(x), we know a translation is represented by a general formula:

g(x) = f(x - a) + b

where a = horizontal shift and b = vertical shift

In this case, there is only a vertical shift of 2 upwards and so we have that a = 0, b = 2

g(x) then becomes:

g(x) = f(x) + 2

`g(x)=x^2\text{ + 2}`