Final answer:
Points on the graph of a function f(x) can be determined on the transformed graphs by applying the transformation rules to the original point. For f(x−5), add 5 to x; for f(x)−6, subtract 6 from y; for f(x+4)+5, subtract 4 from x and add 5 to y.
Step-by-step explanation:
When a function is transformed, points on the graph are shifted according to the transformation rules. Given a point (-5, 4) on the graph of a function f(x), we can find corresponding points on the transformed graphs as follows:
- (a) For the graph of f(x−5), we would add 5 to the x-coordinate of the original point, resulting in the point (0, 4).
- (b) For the graph of f(x)−6, we would subtract 6 from the y-coordinate of the original point, leading to the point (-5, -2).
- (c) For the graph of f(x+4)+5, we would subtract 4 from the x-coordinate and add 5 to the y-coordinate of the original point, giving us the point (-9, 9).
To summarize, the points are as follows:
- (a) The graph of f(x−5) must contain the point (0, 4)
- (b) The graph of f(x)−6 must contain the point (-5, -2)
- (c) The graph of f(x+4)+5 must contain the point (-9, 9)