Graph the linear function. Give its domain and range. $$ f(x)=-5 x+3 $$

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Let's analyze the linear function $$ f(x) = -5x + 3 $$ step by step to determine its domain and range.

### Step 1: Determine the Domain
The domain of a linear function is all real numbers since there are no restrictions on the values that $$ x $$ can take. Therefore, the domain is:

$$
\text{Domain: } (-\infty, \infty)
$$

### Step 2: Determine the Range
Similarly, the range of a linear function is also all real numbers because as $$ x $$ takes on all real values, $$ f(x) $$ will also take on all real values. Thus, the range is:

$$
\text{Range: } (-\infty, \infty)
$$

### Summary
- **Domain:** $$ (-\infty, \infty) $$
- **Range:** $$ (-\infty, \infty) $$

### Graphing the Function
While I cannot plot the graph directly, I can describe how to graph it:

1. **Identify the y-intercept:** Set $$ x = 0 $$:
   $$
   f(0) = -5(0) + 3 = 3
   $$
   So, the y-intercept is at the point $$ (0, 3) $$.

2. **Identify another point:** Choose $$ x = 1 $$:
   $$
   f(1) = -5(1) + 3 = -2
   $$
   So, another point is $$ (1, -2) $$.

3. **Draw the line:** Plot the points $$ (0, 3) $$ and $$ (1, -2) $$ on a coordinate plane and draw a straight line through them, extending in both directions.

This will give you the graph of the linear function $$ f(x) = -5x + 3 $$.
The domain and range of the function $$ f(x) = -5x + 3 $$ are both all real numbers. To graph the function, plot the y-intercept at $$ (0, 3) $$ and another point like $$ (1, -2) $$, then draw a straight line through them.

Graph the linear function. Give its domain and range. \( f(x)=-5 x+3 \)

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