Final answer:
The graph of g(x) = |x + 3| is a V-shaped graph that pivots at the point (-3,0), with two straight lines: one with a positive slope to the right of the pivot and one with a negative slope to the left of the pivot.
Step-by-step explanation:
The student has asked to identify the graph of the function g(x) = |x + 3|. To sketch the graph of this function, we recognize that the absolute value will make all the outputs non-negative, meaning the graph will never go below the x-axis. For values of x where x + 3 is positive, the graph will look like the line y = x + 3.
For values of x where x + 3 is negative, the graph will look like the reflection of the line y = -(x + 3) across the x-axis. The graph will pivot at the point where x + 3 equals zero, specifically at the point (-3,0), creating a V-shape. To sketch this, we plot the pivot point and draw two lines: one with a positive slope of 1 for x values greater than -3, and one with a negative slope of 1 for x values less than -3.