Final answer:
The student's question involves a piecewise function with different formulas for different intervals of x. These pieces are joined together at x = -2, where they both result in the same value, ensuring the function is continuous at that point.
Step-by-step explanation:
The function f described by the student is a piecewise function that depends on the value of x. For x less than -2, the function is defined as f(x) = x - 2. For x greater than or equal to -2, it is defined as f(x) = 3x + 2. To visualize this function, you would draw a line with a slope of 1 and a y-intercept of -2 for all values less than -2, and a line with a slope of 3 and a y-intercept of 2 for all values greater than or equal to -2. The piecewise function changes its formula at the point where x = -2, creating a 'break' in the graph. The function is continuous as it does not jump in value at x = -2 since both expressions equal 4 when x is -2.