Final answer:
To graph the absolute value function f(x) = 2|x+2|+1, plot the vertex at (-2, 1) and draw a V-shape with the lines being twice as steep as the standard absolute value function. Scale the axes up to x=20 and y according to the function's output, and label the graph with 'f(x)' and 'x'.
Step-by-step explanation:
To graph the absolute value function f(x) = 2 ||x+2||+1, you start by understanding the basic shape of an absolute value graph, which is a V-shape. The absolute value expression |x+2| determines where the vertex of the V is located. In this case, the graph will shift 2 units to the left, because we have x+2 inside the absolute value.
The 2 outside affects the steepness or slope of the V, making it twice as steep compared to the standard absolute value function, and the +1 will shift the entire graph up by 1 unit.
First, plot the vertex at (-2, 1). As the input x increases, the output f(x) will increase by a rate of 2 units vertically for every 1 unit horizontally. As x decreases, f(x) decreases at the same rate. Continue plotting points on either side of the vertex until you have a clear V-shape.
Make sure to label your graph with 'f(x)' and 'x' and scale the axes properly, using maximum x values (in this case, at least up to 20 since the domain given is 0 ≤ x ≤ 20) and y values determined by your function.
Since we are restricted to 0 ≤ x ≤ 20, you will only plot the part of the graph where x falls within this interval. After plotting, draw the lines to complete the graph, making sure it's a piecewise linear function with a clear V shape pointing upwards.