Let's analyze the function $h(x) = (x - 7) + 5$ in relation to the parent function $f(x) = x$.

• The expression $(x - 7)$ indicates a horizontal translation of 7 units to the right. This is because subtracting a value inside the function moves the graph to the right.

• The $+5$ added outside the function indicates a vertical translation of 5 units up. Adding a number to the function shifts the graph upwards.

Thus, the two correct answers are:

• A. The graph of $f$ is translated 7 units right.
• D. The graph of $f$ is translated 5 units up.

Would you like further details or have any questions?

Here are five related questions to deepen your understanding:

1. What happens if the function was $h(x) = (x + 7) + 5$?