Answer: - The horizontal shift is in the opposite direction of the sign of the constant being added or subtracted inside the function. In this case, it is a positive horizontal shift of 3 units to the right.
Explanation:
To graph g(x) = f(x-3), you need to shift the graph of f(x) three units to the right. This means that you need to replace all instances of x in f(x) with (x-3) and plot the resulting points on the coordinate plane.
For example, if f(x) = x^2, then g(x) = f(x-3) = (x-3)^2. You can make a table of values and plot the points to obtain the graph of g(x).
Here are some key points to remember:
- If f(x) is a point on the graph of f, then (f(x), x) is a point on the graph of g.
- The shape of the graph of f remains unchanged - only its position shifts.
- The horizontal shift is in the opposite direction of the sign of the constant being added or subtracted inside the function. In this case, it is a positive horizontal shift of 3 units to the right.
I hope this helps!