Two Different Graphs

Suppose that the graph of a function f is known. Expkain how the graph of y = f(x) - 2 differs from the graph of y = f(x - 2).

Let me see.

For the graph of y = f(x) - 2, the graph of y = f(x) is shifted down 2 units on the line x = 0.

For the graph of y = f(x - 2), the graph of y = f(x) is shifted two units to the right on the line y = 0.


You say?

 

Your explanation is on the right track, but there seems to be a slight confusion in your description.

For the graph of =()−2y=f(x)−2, the graph of =()y=f(x) is shifted downward by 2 units. This means that every point on the graph of ()f(x) is lowered by 2 units.

For the graph of =(−2)y=f(x−2), the graph of =()y=f(x) is shifted to the right by 2 units. This means that every point on the graph of ()f(x) is shifted horizontally to the right by 2 units.

So, in summary:

• =()−2y=f(x)−2 shifts the graph of ()f(x) downward by 2 units.
• =(−2)y=f(x−2) shifts the graph of ()f(x) to the right by 2 units.

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1. I am doing a self-study of mathematics.

2. I am not a classroom student.

3. In what way is my description confusing?

I think my answer satisfies the question.

You say?