Let $$ f $$ be the function given by the formula $$ f(x)=5-2 x $$ on the domain $$ D=\{x \mid x=2,3,4,5\} $$. Make a table of the $$ x $$ of 1 and $$ y $$-values to determine the range of f . Then, sketch the graph of t . The range of $$ f $$ is $$ \{\square\} $$. (Use a comma to separate answers as needed.)

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UpStudy AI · Accepted Answer

To determine the range of the function $$ f(x) = 5 - 2x $$ on the specified domain $$ D = \{2, 3, 4, 5\} $$, we will first calculate the $$ y $$-values for each $$ x $$ in the domain.

### Step 1: Calculate $$ y $$-values

1. For $$ x = 2 $$:
   $$
   f(2) = 5 - 2(2) = 5 - 4 = 1
   $$

2. For $$ x = 3 $$:
   $$
   f(3) = 5 - 2(3) = 5 - 6 = -1
   $$

3. For $$ x = 4 $$:
   $$
   f(4) = 5 - 2(4) = 5 - 8 = -3
   $$

4. For $$ x = 5 $$:
   $$
   f(5) = 5 - 2(5) = 5 - 10 = -5
   $$

### Step 2: Create a table of values

Now we can create a table of $$ x $$ and $$ y $$ values:

$$
\begin{array}{|c|c|}
\hline
x & f(x) \
\hline
2 & 1 \
3 & -1 \
4 & -3 \
5 & -5 \
\hline
\end{array}
$$

### Step 3: Determine the range

The $$ y $$-values we calculated are $$ 1, -1, -3, -5 $$. Therefore, the range of $$ f $$ is:
$$
\text{Range of } f = \{1, -1, -3, -5\}
$$

### Final Answer

The range of $$ f $$ is $$ \{1, -1, -3, -5\} $$.

### Step 4: Sketch the graph

To sketch the graph of $$ f $$, we plot the points from the table:

- Point (2, 1)
- Point (3, -1)
- Point (4, -3)
- Point (5, -5)

The graph will show a linear relationship, decreasing as $$ x $$ increases.

### Summary

The range of $$ f $$ is $$ \{1, -1, -3, -5\} $$.
The range of $$ f $$ is $$ \{1, -1, -3, -5\} $$.

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