(2,1) is a point on the graph of y= f (x) . Find the corresponding point on the graph of each of the following functions
a) y= -f (-x) +2
b) y= f (-2(x+9))-7
c) y= f (x-2) +2
d) y= 0.3f (5(x-3))
e) y= 1- f(1-x)
f) y= -f (2(x-8))
a) Well, let's see. If (2,1) is a point on the graph of y = f(x), then to find the corresponding point on the graph of y = -f(-x) + 2, we simply replace x with -2, -f(-(-2)) + 2 = -f(2) + 2. So the corresponding point is (2, -f(2) + 2).
b) Alright, let's do this! If (2,1) is a point on the graph of y = f(x), then to find the corresponding point on the graph of y = f(-2(x+9)) - 7, we substitute x = -2 into f(-2(x+9)) - 7 = f(-2(2+9)) - 7 = f(-20) - 7. So the corresponding point is (-20, f(-20) - 7).
c) Ha, easy peasy! If (2,1) is a point on the graph of y = f(x), then to find the corresponding point on the graph of y = f(x-2) + 2, we just need to replace x with x-2, so f((2-2)) + 2 = f(0) + 2 = f(0) + 2. So the corresponding point is (0, f(0) + 2).
d) This one's a little trickier! If (2,1) is a point on the graph of y = f(x), then to find the corresponding point on the graph of y = 0.3f(5(x-3)), we substitute x = 2 into 0.3f(5(2-3)). Ha, but we also need to simplify the expression inside the function! So, 0.3f(5(-1)), which is equal to 0.3f(-5). So the corresponding point is (-5, 0.3f(-5)).
e) Oh, this one's sneaky! If (2,1) is a point on the graph of y = f(x), then to find the corresponding point on the graph of y = 1 - f(1-x), well, we replace x with (1 - 2) = -1. So, 1 - f(1 - (-1)). Hey, that simplifies to 1 - f(2). So the corresponding point is (2, 1 - f(2)).
f) Aha! If (2,1) is a point on the graph of y = f(x), then to find the corresponding point on the graph of y = -f(2(x-8)), we substitute x = 2 into -f(2(2-8)), which is equal to -f(2(-6)), which simplifies to -f(-12). So the corresponding point is (-12, -f(-12)).
That's all the corresponding points for you! Hope I've brightened up your day!
To find the corresponding point on the graph of each function, we need to substitute the x-coordinate of the given point into each function and find the y-coordinate.
a) y = -f(-x) + 2
To find the corresponding point, we substitute x = 2 and solve for y:
y = -f(-2) + 2
b) y = f(-2(x+9)) - 7
To find the corresponding point, we substitute x = 2 and solve for y:
y = f(-2(2+9)) - 7
c) y = f(x-2) + 2
To find the corresponding point, we substitute x = 2 and solve for y:
y = f(2-2) + 2
d) y = 0.3f(5(x-3))
To find the corresponding point, we substitute x = 2 and solve for y:
y = 0.3f(5(2-3))
e) y = 1 - f(1-x)
To find the corresponding point, we substitute x = 2 and solve for y:
y = 1 - f(1-2)
f) y = -f(2(x-8))
To find the corresponding point, we substitute x = 2 and solve for y:
y = -f(2(2-8))
Please note that without the actual function f(x), we cannot find the exact values for the corresponding points. However, by following the step-by-step process given above, you can substitute the x-coordinate into each function and calculate the corresponding y-coordinate.
To find the corresponding point on the graph of each function, substitute the given point (2,1) into the respective functions one by one. Let's go through each function:
a) y = -f(-x) + 2
Substitute x = 2 into the equation:
y = -f(-2) + 2
To find the corresponding point, we need to find the value of f(-2).
b) y = f(-2(x+9)) - 7
Substitute x = 2 into the equation:
y = f(-2(2+9)) - 7
To find the corresponding point, we need to find the value of f(-20).
c) y = f(x-2) + 2
Substitute x = 2 into the equation:
y = f(2-2) + 2
To find the corresponding point, we need to find the value of f(0).
d) y = 0.3f(5(x-3))
Substitute x = 2 into the equation:
y = 0.3f(5(2-3))
To find the corresponding point, we need to find the value of f(-5).
e) y = 1 - f(1-x)
Substitute x = 2 into the equation:
y = 1 - f(1-2)
To find the corresponding point, we need to find the value of f(-1).
f) y = -f(2(x-8))
Substitute x = 2 into the equation:
y = -f(2(2-8))
To find the corresponding point, we need to find the value of f(-12).
Once you have the value of f(-2), f(-20), f(0), f(-5), f(-1), and f(-12) from the original function f(x), substitute these values into each respective equation to determine the corresponding points on the graphs of the given functions.