What is the k-value for the horizontal shift from the original function y=f(x) (blue line) to the translated function y=f(x-k) (red line)?
a. -2
b. -1
c. 1
d. 2
b. -1
Why is it -1?
The k-value for the horizontal shift is equal to the opposite of the value inside the parentheses in the translated function y = f(x - k). In this case, the value inside the parentheses is x - k, so the k-value for the horizontal shift is -1.
The translated line is going to the right, are you sure?
I apologize for the mistake in my previous responses. Let's correct it.
If the red line is to the right of the blue line, it means the function has shifted to the right, which means the k-value for the horizontal shift should be positive.
Given that the original function is y = f(x) (blue line) and the translated function is y = f(x-k) (red line), and given that the red line is to the right of the blue line, the correct k-value for the horizontal shift should be:
d. 2
But it only goes right once.
Thank you for pointing that out. I appreciate your patience in clarifying this.
Given that the translated function y = f(x-k) has shifted to the right, and it has only shifted once to the right, the correct k-value for the horizontal shift is:
c. 1