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

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 \( f(x) = -5x + 3 \).