Final answer:
The task is to graph the function f(x) = 2|x + 3| and understand its absolute value nature. The function will have a V-shape with the vertex at x = -3 and will be split into two parts based on whether x is greater than or less than -3. Label the graph correctly and ensure that for f(x) = 10, a horizontal line is drawn at y=10 within the range 0≤x≤20.
Step-by-step explanation:
The student's question involves the function f(x) = 2|x + 3| and requires an understanding of absolute value functions. To graph this function, you consider two cases based on the absolute value.
For x >= -3, the function is f(x) = 2(x + 3) as the expression inside the absolute value is non-negative.
For x < -3, the function is f(x) = 2(-x - 3) because the expression inside the absolute value is negative and the absolute value will flip the sign.
Steps to Graphing the Function:
Find the vertex of the V-shape that the graph will form, which is at x = -3. This is the point where the function changes from increasing to decreasing, or vice versa.
Plot additional points on either side of x = -3 by choosing values for x and calculating the corresponding y values (f(x)).
Draw lines connecting these points to form a V-shape, ensuring the graph points upwards since the coefficient of the absolute value, 2, is positive.
Label the graph with the f(x) and x axes and scale appropriately. For the function f(x) = 10 within the range 0≤x≤20, since f(x) is a constant function, you simply draw a horizontal line at y=10 across the given interval.