Which statement correctly describes the effect on the graph of f(x)= √(x + 1) + 2 when it is translated to f(x)= √(x + 1) − 3?

A. The graph is vertically compressed by a factor of 5.
Incorrect. The change is in k not a.

B. The graph is shifted down 5 units.
Correct!

C. The graph is shifted up 5 units.
Incorrect. Look at the k values again and think about where the graph starts to where it is shifted.

D. The graph is shifted 5 units to the left.
Incorrect. The change is in k not h.

Which statement correctly describes the transformation of the parent function f(x) = √x to the square root function graphed below?

A. The graph is translated 4 units up and 5 units to the right.
Incorrect. The graph is translated to the left and down from (0,0).

B. The graph is reflected across the x-axis.
Incorrect. The graph is translated to the left and down from (0,0).

C. The graph is translated 5 units to the left and 4 units down.
Correct!

D. The graph is translated 5 units to the right and 4 units down.
Incorrect. The graph is translated to the left and down from (0,0).

Which statement correctly describes the transformation of the parent function f(x) = 1 x to the rational function graphed below?

A. The graph is translated 1 unit to the right and 1 unit down.
Incorrect. The graph is shifted to the right and up.

B. The graph is translated 1 unit to the right and 2 units up.
Incorrect. It is shifted down 1 unit, not up 2.

C. The graph is translated 1 unit to the right and 1 unit down.
Correct!

D. The graph is translated 1 unit to the left and 2 units down.
Incorrect. The graph is shifted to the right and down.

The rational parent function is translated 3 units to the right and 6 units up. What is the equation of the new graph?

A. f(x) = 1 (x + 3) + 6
Incorrect. This function is shifted to the left.

B. f(x) = 1 (x – 3) + 6
Correct!

C. f(x) = 1 (x + 6) – 3
Incorrect. This function is shifted to the left and down.

D. f(x) = 1 (x – 6) + 3
Incorrect. This function is shifted to the right 6 units and up 3 units.

Which of the following functions describes a transformation of its parent function that has been vertically compressed, horizontally translated to the left, and vertically translated down?

A. f(x) = one-third 1 4 √x + 3 − 8
Correct!

B. f(x) = 4 (x + 3) – 8
Incorrect. This function is has been vertically stretched.

C. f(x) = 4√(x – 3) + 8
Incorrect. This function has been vertically stretched and shifted to the right and up.

D. f(x) = 1 4(x – 3) + 8
Incorrect. This function has been shifted to the right and up.