Graph the following linear function. Give the domain and range. \( f(x)=\frac{1}{4} x+2 \)

The function given is   f(x) = (1/4)x + 2 Step 1: Graphing the Function • The y-intercept occurs when x = 0. Plugging in:   f(0) = (1/4)(0) + 2 = 2.   So, the point (0, 2) is on the graph. • The slope is 1/4, meaning that for every increase of 4 units in x, y increases by 1 unit. For example:   If x = 4, then f(4) = (1/4)(4) + 2 = 1 + 2 = 3, giving the point (4, 3).   Similarly, if x = -4, then f(-4) = (1/4)(-4) + 2 = -1 + 2 = 1, giving the point (-4, 1). • Plot the points (0, 2), (4, 3), and (-4, 1) on a coordinate plane, and draw a straight line through them. Step 2: Domain and Range • Domain:   Since f(x) is a linear function (with no restrictions such as square roots or denominators that could cause division by zero), the domain is all real numbers.   In interval notation: Domain = (–∞, ∞). • Range:   Since the line continues indefinitely in both the upward and downward directions (because the slope is non-zero), the range is also all real numbers.   In interval notation: Range = (–∞, ∞). Summary:  • Graph: A straight line through points (0, 2) and (4, 3) (also through (-4, 1)).  • Domain: All real numbers, i.e., (–∞, ∞).  • Range: All real numbers, i.e., (–∞, ∞). You can visualize the graph by plotting these points on a coordinate grid and drawing a line through them.