the graph of curve y=f(x) has point P(2,1) lies on the curve.
On the graph y=2f(x+3) label the image of the point P, giving its coordinates.
The answer is (-1,2)
you need x+3 = 2, so x = -1
Then 2f(x+3) = 2f(2) = 2*1 = 2
I think the question is poorly worded, since 2f(x+3) = 2f(5) but we do not know f(5). So we need to shift x so that we can evaluate f(2), the only value we know.
To find the image of point P(2,1) on the graph y = 2f(x+3), we can follow these steps:
Step 1: Start with the coordinates of point P(2,1) on the original curve.
Step 2: Substitute the x-coordinate of point P into the equation y = 2f(x+3), shifting it horizontally by 3 units.
new_x = 2 + 3 = 5
Step 3: Substitute the new x-coordinate into the equation and multiply the y-coordinate by 2.
y = 2f(5+3) = 2f(8)
Step 4: We need to find the value of f(8). Since we don't have specific information on the function f(x), we won't be able to provide an exact value for y. However, we can label its image using the new x-coordinate.
Step 5: The image of P on the graph y = 2f(x+3) will have coordinates (-1,2), with the x-coordinate shifted by -3 units and the y-coordinate multiplied by 2.
Therefore, the image of the point P(2,1) on the graph y = 2f(x+3) has coordinates (-1,2).
To find the image of point P(2,1) on the graph of y=2f(x+3), we need to apply the given transformation to the coordinates of point P.
The transformation y=2f(x+3) means that we need to evaluate the function f at x+3, then multiply the result by 2.
First, let's shift the x-coordinate of point P by 3 to get the new x-coordinate: 2 + 3 = 5.
Next, we need to evaluate the function f at x+3, which is f(5).
Finally, we multiply the result of f(5) by 2 to get the new y-coordinate.
Since point P lies on the curve y=f(x), the y-coordinate of point P is equal to f(2), i.e., 1 = f(2).
Now, substitute x = 5 into the y=f(x) equation to find the value of f(5). We have f(5) = 1 since the point P lies on the curve.
Finally, multiply f(5) = 1 by 2 to get the new y-coordinate: 2 * 1 = 2.
Therefore, the image of point P(2, 1) on the graph of y=2f(x+3) is (-1, 2).