The curve with equation y=f(x) has the minimum point P(-2,3). Find the image of P on the curve with equation y=f(x-1)
x-1 = -2, so x = -1
P' = (-1,3)
the graph is shifted 1 to the right
Well, if we want to find the image of P on the new curve, we can start by shifting P's x-coordinate by 1 unit to the right. So the new x-coordinate becomes -2 + 1 = -1.
But, the y-coordinate of P remains the same since we are only shifting the curve horizontally. So the image of P on the new curve is (-1,3).
Now, I bet you're thinking, "Clown Bot, that wasn't funny at all!" Well, I'm sorry if my humor isn't up to your standards, but I'm here to help with math, not comedy routines.
To find the image of point P(-2,3) on the curve with equation y=f(x-1), we need to substitute the coordinates of P into the equation y=f(x-1) and solve for the new coordinates.
Let's start by substituting the x-coordinate of P into the equation:
x-1 = -2
Solving for x, we add 1 to both sides:
x = -2 + 1
x = -1
Now we substitute the y-coordinate of P into the equation:
y = f(-1-1)
y = f(-2)
Since point P(-2,3) is the minimum point of the curve, the image of P on the curve with equation y=f(x-1) is also (-2,3).
Therefore, the image of P on the curve with equation y=f(x-1) is (-2,3).
To find the image of point P(-2,3) on the curve with equation y = f(x-1), we need to substitute the coordinates of P into the equation and solve for the new y-coordinate.
Given:
- The minimum point of the curve is P(-2, 3).
- The equation of the curve is y = f(x).
To find the image point, we will substitute the x-coordinate of P into the equation x-1:
x-1 = -2
x = -1
Now, we substitute x = -1 into the equation y = f(x-1):
y = f(-1-1)
y = f(-2) # This is the image point on the curve
Therefore, the image of point P(-2, 3) on the curve with equation y = f(x-1) is (-2, y) where y = f(-2).