Subjects algebra

Vertical Translation 566058

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Question: Select the correct answer. Consider the function graphed below. If $f$ is translated 4 units down to create $g$, which function represents $g$? g(x) = f(x) + 4 g(x) = f(x - 4) g(x) = f(x) - 4 g(x) = f(x) + 4 graph: exponential curve labeled $f$ in the center-left, with horizontal asymptote near $y = 2$ and increasing steeply to the upper-right; position_hint=center
1. **State the problem:** We have a function $f$ and want to find the function $g$ that results from translating $f$ down by 4 units. 2. **Recall the translation rule:** Translating a function vertically down by $k$ units means subtracting $k$ from the function's output. 3. **Apply the rule:** Since the translation is 4 units down, we subtract 4 from $f(x)$: $$g(x) = f(x) - 4$$ 4. **Check other options:** - $g(x) = f(x) + 4$ translates the graph up by 4 units. - $g(x) = f(x - 4)$ translates the graph 4 units to the right (horizontal shift). 5. **Final answer:** $$\boxed{g(x) = f(x) - 4}$$