Question

If the point (3,3) lies on the graph of y=f(x), what point lies on y=f(x-2)?

Hint: What value of x will make (x-2) equal 3?
A. (5,3)
B. (5,-3)
C. (-5,3)
D. (-5, -3)

Answer 1

Option: A is the correct answer.

A. (5,3)

Explanation:

It is given that:

The point (3,3) lie on the graph of y=f(x)

Now, we are asked to find:

which point lie on the graph of:

y=f(x-2)

The graph is nothing but the translation or the shifting of the function y=f(x) 2 units to the right.

i.e. the coordinates are transformed using the rule:

(x,y) → (x+2,y)

Hence,

(3,3) → (3+2,3)

i.e.

(3,3) → (5,3)

The answer is: Option: A

Answer 2

A. (5, 3)

Explanation:

Making use of the hint:

x -2 = 3

x = 5 . . . . . . add 2

The point (x, 3) is on the graph for x=3.

The point (x-2, 3) is on the graph for x=5, so ...

the graph of (x, f(x-2)) will include the point (5, 3).