The function g(x) = (x2)². The function f(x) = g(x) + 3.
The function f(x) is shifted horizontally
2 units to the right of g(x).
2 units to the left of g(x)
The function f(x) is shifted vertically
3 units up from g(x).
3 units down from g(x)
explain your answer
1. The function f(x) is shifted horizontally 2 units to the right of g(x):
This means that for any given value of x, f(x) will have the same y-value as g(x+2). Essentially, this shifts the entire graph of g(x) to the right by 2 units.
2. The function f(x) is shifted horizontally 2 units to the left of g(x):
In this case, for any given value of x, f(x) will have the same y-value as g(x-2). This means that the graph of f(x) will appear 2 units to the left of the graph of g(x).
3. The function f(x) is shifted vertically 3 units up from g(x):
When the function f(x) is shifted vertically 3 units up from g(x), this means that the entire graph of f(x) will be shifted upwards by 3 units. This can be achieved by adding 3 to the y-values of g(x) at each point.
4. The function f(x) is shifted vertically 3 units down from g(x):
If the function f(x) is shifted vertically 3 units down from g(x), this means that the entire graph of f(x) will be shifted downwards by 3 units. This can be achieved by subtracting 3 from the y-values of g(x) at each point.