https://file.aiquickdraw.com/mathbot/file/1727291528269wgb5huo9.jpg

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 \( h(x) = (x + 7) + 5 \)?


Alicia graphed the function h(x) = (x - 7) + 5. What is the effect on the graph of the parent function f(x) = x? Select TWO correct answers.

Understand how the function h(x) = (x - 7) + 5 translates the parent function f(x) = x by 7 units to the right and 5 units up. This example covers key concepts of graph transformations suitable for students in Grades 8-10.

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