Question

Write a function based on the given parent function and transformations in the given order. Parent function: y = x³ Shift 4.2 units to the left. Reflect across the y-axis. Shift upward 2.3 units.

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asked 2021-03-05
Write a function based on the given parent function and transformations in the given order. Parent function: y = x³
Shift 4.2 units to the left. Reflect across the y-axis. Shift upward 2.3 units.

Answers (1)

2021-03-06
Shift 4.2 units to the left: Add 4.2 to the input x: \(\displaystyle{y}={\left({x}+{4.2}\right)}^{{{3}}}\)
Reflect across the yy-axis: Change the sign of x: \(\displaystyle{y}={\left(−{x}+{4.2}\right)}^{{{3}}}\)
Shift upward 2.3 units: Add 2.3 to the output: \(\displaystyle{y}={\left(−{x}+{4.2}\right)}^{{{3}+{2.3}}}\)
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