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Given the parent function of f(x) = x⁴, what change will occur when the function is changed to f(-2x)?
Graph opens the same way and is narrower
Graph opens the same way and is wider
Graph opens the opposite way and is narrower
Graph opens the opposite way and is wider

Solution:

It is given that

f(x) = x⁴

When f(-2x) = (-2x)⁴ = 16x⁴

f(-2x) = -16x⁴

Graph opens the same way up and is narrower as it gets shrunk on the transformation of f(x) to f(-2x).

transformation of parent function x^4 to 16 x^4

Thus the graph opens the same way and is narrower.

Summary:

Given the parent function of f(x) = x⁴, the graph opens the same way and is narrower when the function is changed to f(-2x).

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Given the parent function of f(x) = x4, what change will occur when the function is changed to f(-2x)? Graph opens the same way and is narrower Graph opens the same way and is wider Graph opens the opposite way and is narrower Graph opens the opposite way and is wider