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.
at original point
x = 2
y = 1
at the new point
x = 2+3 = 5
y = 2 f(5)
(not uniquely defined.)
for example if the function were
f(x) = (1/2) x
then if x = 2 , y = 1. That is P
f(2+3) = f(5) = 2.5
2 f(5) = 5 so the image is (5,5)
but if f(x) = x-1
f(2,1) = (2,1) which is P again
but
x+3 = 5
f(5) = 4
That point is (5,4)
The answer is(1-,2)
To find the image of point P(2,1) on the graph of y=2f(x+3), we need to perform two steps:
Step 1: Shift the point P(2,1) using the equation x' = x + 3 to get the new x-coordinate.
x' = 2 + 3 = 5
Step 2: Evaluate the new y-coordinate by substituting the shifted x-value into the given equation y=2f(x+3).
y = 2f(5)
Now, without knowing the specific function f(x) and being unable to evaluate it directly, we can only conclude that the image of point P on the graph y=2f(x+3) is given by the coordinates (5, 2f(5)).
To determine the exact value of the y-coordinate, you would need to know the specific function f(x) and substitute x=5 into it.