Question
Write an equation for each translation of \( y=|x| \) \( \begin{array}{ll}\text { 34.) } 6 \text { units up } & 35 \text {.) Right } 3 \text { units }\end{array} \)
Ask by Patel Carroll. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
For a translation 6 units up, the equation is \( y = |x| + 6 \). For a translation 3 units to the right, the equation is \( y = |x - 3| \).
Solution
1. For a translation of \( y = |x| \) that shifts the graph **6 units up**, we add 6 to the original function:
\[
y = |x| + 6
\]
2. For a translation of \( y = |x| \) that shifts the graph **3 units to the right**, we replace \( x \) with \( x - 3 \):
\[
y = |x-3|
\]
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Simplify this solution Bonus Knowledge
To translate the graph of \( y = |x| \) six units up, you'll need to add 6 to the equation. So, the new equation becomes \( y = |x| + 6 \). For a rightward translation of three units, you'll replace \( x \) with \( x - 3 \) in the equation. Thus, the equation becomes \( y = |x - 3| \).
