Question

See attached problem; graph , state the domain and range.The graph has a pic of f(x)Part A.

Answer 1

You know that the parabola shown in the Coordinate Plane is the function:

`f(x)`

According to the Transformation Rules for Functions, when:

`f(x-h)`

The function is shifted "h" units to the right.

Then, since the new function is:

`f(x-2)`

The new graph will be similar to the original graph but shifted 2 units to the right.

Knowing, you can graph the new function:

- Choose 5 points on the original function:

`\begin{gathered} (0,0) \\ (-2,4) \\ (-3,9) \\ (2,4) \\ (3,9) \end{gathered}`

- Translate them 2 units to the right by adding 2 to each x-coordinate:

`\begin{gathered} (2,0) \\ (0,4) \\ (-1,9) \\ (4,4) \\ (5,9) \end{gathered}`

- The parabola must pass through these points.

See the graph attached:

Since a parabola continues up toward both sides, you can determine that its Domain is:

`Domain\colon-\inftySince the parabola continues upward and the minimum value of`

You can conclude that its Range is:

`Range\colon y\ge0`

Hence, the answer is:

- Graph:

- Domain:

`Domain\colon-\infty- Range:[tex]Range\colon y\ge0`