Determine if reversing the order of the following two transformations can produc

Question

Determine if reversing the order of the following two transformations can produce a different result.

reflection in the x dash axisreflection in the x-axis; horizontal shifthorizontal shift

1) The result of a reflection in the x dash axisreflection in the x-axis followed by a horizontal shifthorizontal shift would most naturally be denoted by??

2) The result of a horizontal shifthorizontal shift followed by a reflection in the x dash axisreflection in the x-axis would most naturally be denoted by??

3)Therefore, reversing the order does not OR does change the final result??

Explanation / Answer

The result of a reflection in the x dash axisreflection in the x-axis followed by a horizontal shifthorizontal shift would most naturally be denoted by :

Reflection in x-axis means change to negative
So, f(x) --> -f(x)

Horiz shift would be x changing to x-a

So, -f(x - a) ---> Final ans

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2) The result of a horizontal shifthorizontal shift followed by a reflection in the x dash axisreflection in the x-axis would most naturally be denoted by??

Horiz shift is first done by f(x - a)

And now, reflect it abt x-axis :
So, change f(x-a) to

-f(x-a) ---> final ans

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3)
DOES NOT

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