What value represents the horizontal translation from the graph of the parent function f(x) = x^2 to the graph of the function g(x) = (x – 4)^2 + 2?
Same caveat as previously:
Vertical = +2
Horizontal = +4
To determine the horizontal translation from the graph of the parent function f(x) = x^2 to the graph of the function g(x) = (x – 4)^2 + 2, we need to identify the change in the x-values.
In the given equation g(x) = (x – 4)^2 + 2, we can see that the x-values of the function have been shifted 4 units to the right compared to the parent function f(x) = x^2.
To understand this, consider the term (x – 4) in the equation g(x) = (x – 4)^2 + 2. In the parent function f(x) = x^2, the x-values are not modified. However, in the function g(x), the expression (x – 4) indicates that we subtract 4 from each x-value before squaring it.
Therefore, the horizontal translation from the graph of f(x) = x^2 to g(x) = (x – 4)^2 + 2 is 4 units to the right.