Final answer:
None of the given options A through D are correct as a linear function with a non-zero slope cannot have the same output for two different inputs. The correct equation of a line that satisfies the conditions f(0) = 3 and f(-6) = 3 is a horizontal line y = 3, which is not listed. The correct answer is option B .
Step-by-step explanation:
The student's question pertains to finding a linear function that satisfies the conditions f(0) = 3 and f(-6) = 3. A linear function is of the form f(x) = mx + b, where m is the slope and b is the y-intercept. The fact that f(0) = 3 for either equation suggests that the y-intercept (b) must be 3. Furthermore, to satisfy the condition f(-6) = 3, we have to find a function where the input of -6 does not change the output value of 3. This implies that the slope (m) of the function should be 0 since a nonzero slope would change the output value as x changes.
Let's evaluate each option given to the student:
By process of elimination, none of the equations listed (A through D) actually satisfies both conditions, as a linear function with a non-zero slope cannot have the same value for two different x values (0 and -6, in this case). However, this may be a trick question—the correct answer would be an equation of the horizontal line y = 3. Since none of the options are of that form, the likely correct answer would indicate that none of the given options satisfy both conditions.