Let f(x)=4√x
If g(x) is the graph of f(x) shifted up 3 units and right 2 units, write a formula for g(x).
g(x)=
to shift up 3 we simply add 3,
so far:
y = 4√x + 3
to move to the right 2, we replace the x with (x-2)
final :
g(x) = 4√(x-2) + 3
check: on Wolfram
https://www.wolframalpha.com/input/?i=graph+y+%3D+4%E2%88%9Ax+%2C+y+%3D+4%E2%88%9A%28x-2%29+%2B+3
( look only at the curves in quadrant I, ignore the "imaginary" parts of the graph )
moving up
if x = 0, g = 3
g(x) = 3 + f(x)
moving sideways
g( x) = f(x-2)
so
g(x) = 3 + f(x-2)
g(x) = 3 + 4 sqrt ( x-2)
g(x) = 4√(x-2) + 3
Why did the mathematician skip lunch?
Because he already had an irrational number!
To find the formula for the graph of g(x), which is the graph of f(x) shifted up 3 units and right 2 units, we need to adjust the function f(x) accordingly.
First, let's break down the adjustments:
- Shifting up by 3 units means adding 3 to the y-coordinate of each point on the graph.
- Shifting right by 2 units means subtracting 2 from the x-coordinate of each point on the graph.
So, to shift f(x) up by 3 units, we add 3 to f(x). And to shift f(x) right by 2 units, we subtract 2 from x.
Therefore, the formula for g(x) is:
g(x) = 4√(x - 2) + 3
This formula represents the graph of f(x) shifted up 3 units and right 2 units.