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Which graph shows the transformation of the function f(x)=e^x when the function is translated 3 units to the right, vertically compressed by 1/4, and translated 6 units down?

Which graph shows the transformation of the function fxex when the function is translated 3 units to the right vertically compressed by 14 and translated 6 unit class=

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Answer: Top Right

Explanation:

Write the function:

[tex]f(x)=\frac{1}{4}e^{x-3}-6[/tex]

y-intercept:

[tex]f(0)=\frac{1}{4}e^{-3}-6\approx-5.99[/tex]

x-intercept:

[tex]0=\frac{1}{4}e^{x-3}-6\\24=e^{x-3}\\\ln 24=x-3\\x=\ln 24 +3 \approx 6.18[/tex]

The graphs that matches the above x- and y-intercepts is the top-right choice.

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