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Using y=1/x as the parent function, make your own transformations (5 units right, reflect on x axis, 2 units down, horizontal compression with factor 2). Then graph and state domain and range.

User WedaPashi
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First, we have a translation of 5 units right. That means the value of x is decreased by 5 units (x' = x - 5)

So we have:


y=(1)/(x-5)

Then, we have a reflection over the x-axis, which means the value of the function changes signal (y' = -y)


y=-(1)/(x-5)

Finally, we have a translation of 2 units down, which means the value of the function is decreased by 2 units (y' = y - 2)


y=-(1)/(x-5)-2

Adding a horizontal compression by a factor of 2 means the value of x will be multiplied by 2 (x' = 2x)


y=-(1)/(2x-5)-2

Graphing this function, we have:

The domain is all values x can assume. Since we have a fraction, its denominator can't be zero, so:


\begin{gathered} 2x-5\\e0 \\ 2x\\e5 \\ x\\e2.5 \end{gathered}

So the domain is:


(-\propto,2.5)\cup(2.5,\propto)

The range is all values y can assume. Since the fraction can't have a value of zero, we have:


\begin{gathered} y\\e0-2 \\ y\\e-2 \end{gathered}

So the range is:


(-\propto,-2)\cup(-2,\propto)

Using y=1/x as the parent function, make your own transformations (5 units right, reflect-example-1
User Uladzislau Vavilau
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