Let f(x)=4 sqrt(x). If g(x) is the graph of f(x) shifted down 2 units and right 1 unit, write a formula for g(x) like this g(x)=
Please help ASAP I don't understand this at all!!! :(
if you have y=f(x)
to shift right by h, replace x with x-h
to shift up by k, replace y by y-k
So, to shift down 2 (up by -2) and right 1,
y = 4√x becomes
y+2 = 4√(x-1)
or,
g(x) = 4√(x-1) - 2
go to some handy online graphing app, like desmos.com or wolframalpha.com, and play around with making similar changes till you are comfortable with things.
Alright, I'll do my best to help you out! So, we start with the function f(x) = 4√(x). To shift it down 2 units, we subtract 2 from the original function, resulting in f(x) - 2. To shift it right 1 unit, we replace x with (x - 1), resulting in f(x - 1).
So, the formula for g(x) would be g(x) = f(x - 1) - 2.
Now you can plug in any value of x into this formula to find the corresponding y-coordinate on the shifted graph! I hope this clarifies things for you. If you have any more questions, feel free to ask!
To shift the graph of f(x) down 2 units, we need to subtract 2 from the function f(x). To shift it right 1 unit, we need to replace x with (x - 1). So the formula for g(x) would be:
g(x) = 4 sqrt(x - 1) - 2
Don't worry, I'm here to help! Let's break it down step by step.
The function f(x) = 4√(x) represents a square root function with a coefficient of 4.
To create the function g(x) by shifting f(x) down 2 units and right 1 unit, we need to apply two transformations: a vertical shift and a horizontal shift.
1. Vertical Shift: To shift f(x) down 2 units, we subtract 2 from the original function f(x). So, the first part of the formula for g(x) is f(x) - 2.
2. Horizontal Shift: To shift f(x) right 1 unit, we need to shift the input value (x) by 1 unit in the opposite direction. So, we replace the original x in the formula with (x - 1). Therefore, the complete formula for g(x) is (f(x - 1)) - 2.
Combining these two transformations, we get the formula for g(x) as g(x) = 4√(x - 1) - 2.
It's important to note that the transformations are applied in a specific order: horizontal transformations (shifting) first, followed by vertical transformations (stretching/compressing).