The point (-7,0) is on the graph of the function y=f(x). Which point cannot be on the graph of y=f(x)?
A. (0,0)
B. (0,-7)
C. (-7,-7)
D. (7,0)
C
review what makes a function
To determine which point cannot be on the graph of y=f(x), we need to understand what it means for a point to lie on the graph of a function.
A point (x, y) is considered to be on the graph of a function f if and only if f(x) = y. In other words, substituting the x-coordinate into the function should give us the corresponding y-coordinate.
Let's test each point given in the answer choices by substituting the x-coordinate into f(x):
A. (0,0)
Substituting x=0 into f(x) gives f(0) = 0. So, this point can be on the graph.
B. (0,-7)
Substituting x=0 into f(x) gives f(0) = -7. Since y needs to be -7 according to the given point, this point can be on the graph.
C. (-7,-7)
Substituting x=-7 into f(x) gives f(-7) = -7. So, this point can be on the graph.
D. (7,0)
Substituting x=7 into f(x) gives f(7) = 0. However, the given function f(7) should yield a y-coordinate of 0, not the given y-coordinate of 0. Therefore, this point cannot be on the graph.
Therefore, the point that cannot be on the graph of y=f(x) is D. (7,0).
To answer this question, we need to check if the given points satisfy the equation of the graph y = f(x). Let's substitute the x and y values into the equation and see which point does not satisfy it.
For point A (0,0):
When we substitute x = 0 into y = f(x), we get y = f(0). So, the coordinates of point A are (0, f(0)). From the given information, we know that the point (-7,0) is on the graph of y = f(x). Therefore, point A (0,0) can be on the graph of y = f(x).
For point B (0,-7):
When we substitute x = 0 into y = f(x), we get y = f(0). So, the coordinates of point B are (0, f(0)). Since we know that the point (-7,0) is on the graph of y = f(x) and not (-7,-7), point B (0,-7) does not satisfy the equation and cannot be on the graph of y = f(x).
For point C (-7,-7):
When we substitute x = -7 into y = f(x), we get y = f(-7). So, the coordinates of point C are (-7, f(-7)). From the given information, we know that the point (-7,0) is on the graph of y = f(x). Therefore, point C (-7,-7) can be on the graph of y = f(x).
For point D (7,0):
When we substitute x = 7 into y = f(x), we get y = f(7). So, the coordinates of point D are (7, f(7)). Since we know that the point (-7,0) is on the graph of y = f(x) and not (7,0), point D (7,0) does not satisfy the equation and cannot be on the graph of y = f(x).
To summarize:
Point B (0,-7) and point D (7,0) cannot be on the graph of y = f(x).
Hence, the correct answer is B. (0,-7).