Question

The function f (x) is transformed using the function rule f (x-2)+5. Rene thinks that the graph of the transformed is shifted horizontally 5 units to the left and vertically 2 units up. Explain why he is wrong.

Answer 1

Rene is wrong because the function rule f(x-2)+5 shifts the graph horizontally 2 units to the right and vertically 5 units up, not the opposite.

Step-by-step explanation:

Rene is wrong because the function rule f(x-2)+5 does not shift the graph horizontally 5 units to the left and vertically 2 units up. Instead, it shifts the graph horizontally 2 units to the right and vertically 5 units up. This is because when we replace x with (x-2) in the function, it causes the graph to shift in the opposite direction. Similarly, adding 5 to the function causes a vertical shift upwards.

For example, let's consider the original graph of f(x) = x. If we apply the function rule f(x-2)+5, the new graph will be f(x-2)+5 = x-2+5 = x+3. This means that every point on the graph of f(x) will move 2 units to the right and 5 units up to create the new graph.