Question

Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function.

y = f(x + 1)

Answer 1

Well, we know that 4 = f(2) and that all we know about f.

So what are the only values of x and y can we use in
y = f(x+1) ?

Answer 2

A) (1, 4)
B) (2, 5)
C) (3, 4)
or
D) (2, 3)

Answer 3

Forget the possible answers now and think. We only know ONE thing about this function f(x): that (x,y) = (2,4) is on the graph.

So now that we need to find a point on the graph of
y = f(x+1)
what can be the ONLY choice for y?

Answer 4

y = f(x+1) and
4 = f(2),

hence y must be .... what?

Answer 5

4

Answer 6

Yep. Now what must x be?

Answer 7

(mathematical eagles: the "must" here isn't quite right, but for this question it's fine.)

Answer 8

y=f(x+1) has ordered pairs of the form (x+1,y)
y=f(x) has ordered pairs of the form (x,y)
we know a point on y=f(x) which is (2,4)
so when does (2,4)=(x+1,y)
you said y=4
so we have
(2,4)=(x+1,4)