Question

The function H is defined as follows for the domain given.
h (x) = 1 - 2x, domain = {-3, -2, 1, 5}
Write the range of H using set notation. Then graph H.

Answer 1

To find the range of the function \( h(x) = 1 - 2x \) for the specified domain \( \{-3, -2, 1, 5\} \), we will calculate the value of \( h(x) \) for each element in the domain:

1. For \( x = -3 \):
\[
h(-3) = 1 - 2(-3) = 1 + 6 = 7
\]

2. For \( x = -2 \):
\[
h(-2) = 1 - 2(-2) = 1 + 4 = 5
\]

3. For \( x = 1 \):
\[
h(1) = 1 - 2(1) = 1 - 2 = -1
\]

4. For \( x = 5 \):
\[
h(5) = 1 - 2(5) = 1 - 10 = -9
\]

Now we compile the output values:
- \( h(-3) = 7 \)
- \( h(-2) = 5 \)
- \( h(1) = -1 \)
- \( h(5) = -9 \)

Thus, the range of \( h \) can be written using set notation:
\[
\text{Range}(h) = \{-9, -1, 5, 7\}
\]

### Graph of \( h \)

Now, we will represent the function in graph form. Given that \( h \) is defined for a discrete set of points, the graph will consist of points corresponding to the domain and their associated outputs.

\[
\text{Points to plot: } (-3, 7), (-2, 5), (1, -1), (5, -9)
\]

Here's a rough sketch of the graph:

```
|
8| *
7| |
6| |
5| * |
4| |
3| |
2| |
1| |
|_____________________
-3 -2 0 1 2 3 4 5
| *
-1| |
| |
-2| |
-3| |
-4| |
-5| |
-6| |
-7| |
-8| |
-9| *
```

Each asterisk (*) represents a point on the graph of \( h(x) \) corresponding to its calculated values. The points are:
- (-3, 7)
- (-2, 5)
- (1, -1)
- (5, -9)

That's the entire analysis including calculation of the range and a graph representation of the function!