Final answer:
The student asked to determine which points are on the graph of f(x) = 2x + 3. By substituting the x-values into the function, it was found that points (0,3), and (-1,1) are on the graph, while points (-4,-6) and (0,-2) are not.
Step-by-step explanation:
To determine whether the given points are on the graph of f(x) = 2x + 3, we can plug the x-value of each point into the function and see if the y-value matches with the one given in the point.
- A) (0,3): If we plug the x-value 0 into the equation we get f(0) = 2(0) + 3 = 3, which matches the y-value of point A. So, this point is on the graph.
- B) (-4,-6): f(-4) = 2(-4) + 3 = -8 + 3 = -5, which does not match the y-value of point B. So, this point is not on the graph.
- C) (0,-2): Since f(0) = 3 as calculated for point A, the y-value of -2 does not match. Thus, this point is not on the graph.
- D) (-1,1): f(-1) = 2(-1) + 3 = -2 + 3 = 1, which matches the y-value of point D. So, this point is on the graph.
The points (0,3) and (-1,1) are on the graph of f(x) = 2x + 3. Points (-4,-6) and (0,-2) are not on the graph.