Question
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Given the function \( f(x)=x^{3} \), how many units and in what direction will the graph of \( g(x)=f(x)-3 \) be shifted? Option \#1: The graph will shift vertically 3 units down. Option \#2: The graph will shift vertically 3 units up. Option \#3: The graph will shift horizontally 3 units to the left. (1 point) The best answer to the question is Option \#

Ask by Ward Mccoy. in the United States
Jan 23,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

The graph of \( g(x) = x^3 - 3 \) is shifted **3 units down**.

Solution

The best answer to the question is **Option #1**. **Explanation:** The function \( g(x) = f(x) - 3 = x^3 - 3 \) represents a vertical shift of the original function \( f(x) = x^3 \). Subtracting 3 from the function decreases all output values by 3, which means the graph is shifted **vertically downward by 3 units**. **Correct Answer:** Option #1

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The Deep Dive

The graph of \( g(x) = f(x) - 3 \) represents a vertical shift of the original function \( f(x) = x^3 \). Since we've subtracted 3 from \( f(x) \), the entire graph will move down by 3 units. So, Option #1 is correct: the graph will shift vertically 3 units down! Now, if you want to visualize this, think of the original cubic graph \( y = x^3 \) soaring upwards. When you shift it downwards, it's like pulling it closer to the ground but keeping its shape intact—just a “lower altitude” version of its former self! So, grab your graph paper and see how it dances differently after the drop!

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