Question

analyzing relationships
in exercises 13–16, match the
function with the correct
transformation of the graph
of ( f ). explain your reasoning.

1. ( y = f(x - 1) )
2. ( y = f(x) + 1 )
3. ( y = f(x - 1) + 1 )
4. ( y = f(x + 1) - 1 )

a.

b.

c.

d.

Explanation:

1. For $y=f(x-1)$: Horizontal shift right 1 unit. The vertex of $f$ moves right, matching graph C.
2. For $y=f(x)+1$: Vertical shift up 1 unit. The vertex of $f$ moves up, matching graph A.
3. For $y=f(x-1)+1$: Right 1, up 1. Vertex shifts right and up, matching graph D.
4. For $y=f(x+1)-1$: Left 1, down 1. Vertex shifts left and down, matching graph B.

Answer:

1. C
2. A
3. D
4. B