Graph the linear function. Give its domain and range. \( f(x)=-3 x+6 \)

We are given the linear function   f(x) = –3x + 6 Step 1. Find key points:  • To find the y-intercept, set x = 0:   f(0) = –3(0) + 6 = 6   So the y-intercept is at (0, 6).  • To find the x-intercept, set f(x) = 0:   0 = –3x + 6 ⟹ –3x = –6 ⟹ x = 2   So the x-intercept is at (2, 0). Step 2. Graphing the Function:  1. Plot the y-intercept (0, 6) on the coordinate plane.  2. Plot the x-intercept (2, 0).  3. Draw a straight line through these two points because the graph of a linear function is a straight line.  4. You can extend the line in both directions. Step 3. Domain and Range:  • Domain: For any linear function, x can be any real number. Thus, the domain is (–∞, ∞).  • Range: Since the line continues without end upwards and downwards (despite the negative slope), the range is also (–∞, ∞). Summary:  • Graphing: The line passes through (0, 6) and (2, 0), with a slope of –3.  • Domain: All real numbers, (–∞, ∞).  • Range: All real numbers, (–∞, ∞).