The function g (x) = (x - 2)^2. The function f(x) = g (x) + 3.

Question

the function f (x) is shifted horizontally ______

the function f(x) is shifted vertically ________

Answer 1

The function f(x) is shifted horizontally 2 units to the right.

The function f(x) is shifted vertically 3 units up.

Answer 2

explain

Answer 3

Sure!

For the horizontal shift, when we add 3 to g(x), it means that the entire function g(x) is shifted vertically by 3 units. This means that the x-values do not change, only the y-values are affected. Since g(x) = (x - 2)^2, adding 3 to g(x) shifts the entire graph vertically 3 units up. Therefore, the function f(x) is shifted 3 units up compared to g(x), but horizontally, it remains in the same position because we are adding to y-values, not x-values.

As for the vertical shift, since the entire g(x) function is shifted up by 3 units to form f(x), the vertical shift is 3 units up. This means that the entire graph moves up 3 units with respect to the x-axis.

Answer 4

explain it with less words and more simple

Answer 5

The function f(x) is shifted horizontally 2 units to the right because adding 3 to g(x) shifts the graph up by 3 units, not left or right.

The function f(x) is shifted vertically 3 units up because adding 3 to g(x) moves the graph up by 3 units compared to g(x).