The graph of y = f(x - 3) is a _____ of the graph of y = f(x)
A. Shift 3 units to the right
B. Shift 3 units up
C. Scale change of the output by a factor of -3
D. Scale change of the input by a factor of 3
If the point (1,3) is on the graph of y = f(x), then what is the corresponding point on the graph of y = -2f(c)?
A. (-2,-6)
B. (1,-6)
C: (-2,3)
D. (1,3)
well, say y = x
if x = 0, y = 0
y = x-3
if x = 3 y =0
moved 3 rightt
What about the other question?
3 = f(1)
if c = 1, y = -2*3 = -6
(1, -6)
And 1. Is shift 3 units to the right
And 2 is?
Thanks
To determine the answer, let's analyze the given options and compare them to the given equations:
A. Shift 3 units to the right: This option suggests that the graph of y = f(x - 3) is obtained by shifting the original graph 3 units to the right. This means that every point (x, y) on the graph of y = f(x) is transformed into a new point (x - 3, y) on the graph of y = f(x - 3). Therefore, if the original point is (1,3), when shifted 3 units to the right, the new point will be (1 - 3, 3) = (-2,3). This option doesn't match with the given equation, so it is not correct.
B. Shift 3 units up: This option suggests that the graph of y = f(x - 3) is obtained by shifting the original graph 3 units up. This means that every point (x, y) on the graph of y = f(x) is transformed into a new point (x, y + 3) on the graph of y = f(x - 3). Again, this option doesn't match with the given equation, so it is not correct.
C. Scale change of the output by a factor of -3: This option suggests that the graph of y = f(x - 3) is obtained by scaling the output of the original graph by a factor of -3. This means that every point (x, y) on the graph of y = f(x) is transformed into a new point (x, -3y) on the graph of y = f(x - 3). This option doesn't match with the given equation, so it is not correct.
D. Scale change of the input by a factor of 3: This option suggests that the graph of y = f(x - 3) is obtained by scaling the input of the original graph by a factor of 3. This means that every point (x, y) on the graph of y = f(x) is transformed into a new point (3x, y) on the graph of y = f(x - 3). This option matches with the given equation, so it is the correct answer.
Therefore, the answer to the first question is: D. Scale change of the input by a factor of 3.
Now, let's move on to the second question:
To determine the corresponding point on the graph of y = -2f(c), we need to substitute the x-coordinate of the original point (1,3) into the equation -2f(c) and check for the resulting y-coordinate.
Substituting x = 1 into the equation -2f(c), we have:
y = -2f(1)
Since the original point (1,3) is on the graph of y = f(x), we know that f(1) = 3. Therefore, substituting this value, we get:
y = -2(3)
y = -6
So, the corresponding point on the graph of y = -2f(c) is (1, -6).
Therefore, the answer to the second question is: B. (1,-6).