Question

The black graph is the graph of

y = f(x). Choose the equation for the
red graph.

a. y = f(x + 3)
b. y = f(x – 3)
c. y + 3 = f(x)
d. y - 3 = f(x)

Answer 1

9514 1404 393

Answer:

b. y = f(x -3)

Explanation:

The translation right h and up k units is ...

y -k = f(x -h)

Here, the red graph is translated right 3 and up 0, so the translated function is ...

y = f(x -3)

_____

Additional comment

You can check this if you like by listing a couple of corresponding points:

y = f(x)

1 = f(-3) . . . . left-most point on black graph.

The corresponding point on the red graph is (0, 1). Putting this into the equation (b), we get ...

1 = f(0 -3) = f(-3) . . . . . correct value for f(-3)