How do you use the graph of $f (x) = 10^{x}$ $f(x)=10^x$ to describe the transformation of $g (x) = 10^{- x + 3}$ $g(x)=10^(-x+3)$ ?

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How do you use the graph of $f (x) = 10^{x}$ $f(x)=10^x$ to describe the transformation of $g (x) = 10^{- x + 3}$ $g(x)=10^(-x+3)$ ?

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Answer 1 · 2017-04-25T06:57:07

$g (x) = f (- (x - 3))$ $g(x) = f(-(x-3))$

A translation by 3 in the x direction followed by a reflection.

Explanation:

I hate these combined transformation type questions. What you need to look at here is the argument for the function.

$f (x) = 10^{x}$ $f(x)=10^x$

$g (x) = 10^{- x + 3}$ $g(x)=10^(-x+3)$

so it follows that

$g (x) = f (- x + 3)$ $g(x)=f(-x+3)$

We should know that $f (- x)$ $f(-x)$ is a reflection of $f (x)$ $f(x)$ and $f (x - a)$ $f(x - a)$ is a translation of $f (x)$ $f(x)$ by $a$ $a$ in the x direction (sorry, can't seem to write vectors on here). The difficult thing to get your head around is the order in which the transformations are applied.

By writing $- x + 3$ $-x+3$ as $- (x - 3)$ $-(x-3)$ it should help you to realise the shift.
graph{10^(-x+3) [-1.077, 6.523, -0.44, 3.36]}

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How do you use the graph of $f (x) = 10^{x}$ $f(x)=10^x$ to describe the transformation of $g (x) = 10^{- x + 3}$ $g(x)=10^(-x+3)$ ?

1 Answer

Explanation:

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How do you use the graph of f(x)=10xf(x)=10^x to describe the transformation of g(x)=10−x+3g(x)=10^(-x+3)?

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Explanation:

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How do you use the graph of $f (x) = 10^{x}$ $f(x)=10^x$ to describe the transformation of $g (x) = 10^{- x + 3}$ $g(x)=10^(-x+3)$ ?