Final answer:
The student has correctly identified the x-intercept of the function at (-4,0) but claims there is no y-intercept, which could be valid depending on the nature of the function. The x-intercept is where the graph crosses the x-axis, and the absence of a y-intercept would occur if the function is parallel to the y-axis.
Step-by-step explanation:
Finding X and Y Intercepts of a Function
The question involves finding the x-intercept and y-intercept of a given function. The x-intercept of a function is the point where the graph of the function crosses the x-axis, which occurs when the y-value is zero. The y-intercept is the point where the graph crosses the y-axis, at x=0.
According to the student's solution, the x-intercept is given as (-4,0), which means the function crosses the x-axis at x = -4. This is confirmed, as the coordinates satisfy the condition for an x-intercept (y = 0). However, the student states there is no y-intercept, which implies that the function never crosses the y-axis. This could happen if the function is defined in such a way that it is never equal to zero when x is zero, or the graph is a vertical line, which means it's parallel to the y-axis and hence does not have a y-intercept.
The concept of y-intercept is important as it represents the value of the function when the x-value is zero. However, in some contexts, such as when considering time as the independent variable, a year 0 does not exist, and thus a y-intercept would also not exist conceptually.
In conclusion, if a student's solution states an x-intercept at (-4,0) and no y-intercept, this is plausible depending on the context and definition of the function.