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The function f(x) = x2 is transformed to f(x) = −1.4x2. Which statement describes the effect(s) of the transformation on the graph of the original function?
A) The parabola is wider and reflected across the x-axis.
B) The parabola is wider and reflected across the y-axis.
C) The parabola is narrower and reflected across the x-axis.
D) The parabola is narrower and reflected across the y-axis.

The function fx x2 is transformed to fx 14x2 Which statement describes the effects of the transformation on the graph of the original function A The parabola i class=

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Answer:

C) The parabola is narrower and reflected across the x-axis.

Step-by-step explanation:

The original parabola has equation:

[tex]f(x) = {x}^{2} [/tex]

The transformed parabola has equation

[tex]f(x) = - 1.4 {x}^{2} [/tex]

How wide the graph is can be determined by the absolute value of the coefficient.

The smaller the absolute value of the coefficient, the wider the graph.

Since

[tex] |1| \: < \: | - 1.4| [/tex]

The original graph is wider than the transformed graph.

Also the negative factor tells us there is a reflection in the x-axis.

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