the graph of reciprocal parent function, f(x)=1/x, is shifted 3 units up and 4 units to the right to create the graph of g(x). what function is g(x)?
a. g(x)=1/ x+3 +4
b. g(x)=1/ x-3 +4
c. g(x)=1/ x+4 +3
d. g(x)=1/ x-4+3
y = 1/x
Y - 3 = 1 / (X-4)
Y = 1 / (X-4) + 3
Help
I need help with my math homework
Oh, I love graphs! Let me help you solve this one with a joke.
Why did the function go to therapy?
Because it needed a shift in perspective!
Alright, let's get back to the question. To shift the reciprocal parent function 3 units up and 4 units to the right, we need to adjust the equation.
The correct function for g(x) would be option C: g(x) = 1/(x + 4) + 3.
Remember, the shift is in the opposite direction of the sign, so it's (x + 4), and we add 3 to shift it up. Well done!
To shift the graph of the reciprocal parent function f(x) = 1/x, 3 units up and 4 units to the right, you need to adjust the equation accordingly.
When you shift the graph 3 units up, you add 3 to the equation. This means the equation becomes f(x) = 1/x + 3.
Similarly, when you shift the graph 4 units to the right, you need to substitute (x - 4) instead of just x. This means the equation becomes f(x) = 1/(x-4).
Combining both adjustments, the function for g(x) after the shift becomes g(x) = 1/(x-4) + 3.
Therefore, the correct option would be:
d. g(x) = 1/(x-4) + 3.