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The equation becomes y = 5(2^-(x-2))+5 if the equation for the graph that has been reflected in the y-axis, given a vertical stretch by a factor of 5, translated 2 units right and 5 units down.
It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have equation:
[tex]\rm y = 2^x[/tex]
Plug x → -x to reflected in the y-axis.
The function becomes:
[tex]\rm y = 2^-^x[/tex]
For vertical stretch, multiply the function by 5.
The function becomes:
[tex]\rm y\ =\ 5\left(2^{-x}\right)[/tex]
For translate 2 units, right plug x → (x-2)
[tex]\rm y\ =\ 5\left(2^{-(x-2)}\right)[/tex]
For translate 5 units, up add 5 to the function.
The function becomes:
[tex]\rm y\ =\ 5\left(2^{-(x-2)}\right)+5[/tex]
Thus, the equation becomes y = 5(2^-(x-2))+5 if the equation for the graph that has been reflected in the y-axis, given a vertical stretch by a factor of 5, translated 2 units right and 5 units down.
Learn more about the function here:
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