3. Which function deseribes the graph of \( f(x) \) Hamslated 10 thnis to the hight A. \( f(x+10) \) B. \( f(x-10) \) C. \( f(x)+10 \) D. \( f(x)-10 \)

To determine which function describes the graph of \( f(x) \) translated 10 units upward, we need to understand how vertical translations work in function notation. 1. **Vertical Translation**: When a function \( f(x) \) is translated vertically, we add or subtract a constant to the function itself: - If we add a constant \( k \) to the function, \( f(x) + k \), the graph moves upward by \( k \) units. - If we subtract a constant \( k \) from the function, \( f(x) - k \), the graph moves downward by \( k \) units. 2. **Given Problem**: We want to translate the graph of \( f(x) \) upward by 10 units. 3. **Applying the Concept**: - To move the graph of \( f(x) \) upward by 10 units, we would use the expression \( f(x) + 10 \). Now, let's analyze the options provided: - A. \( f(x+10) \): This represents a horizontal shift to the left by 10 units. - B. \( f(x-10) \): This represents a horizontal shift to the right by 10 units. - C. \( f(x) + 10 \): This represents a vertical shift upward by 10 units. - D. \( f(x) - 10 \): This represents a vertical shift downward by 10 units. Thus, the correct answer is: **C. \( f(x) + 10 \)**.