How do you identify the transformation of #h(x)=-2sqrt(x-4)#?

1 Answer
Rachel
Mar 21, 2018

Let's look at the parent function, #y = sqrtx#

graph{y = sqrtx}

Now let's shift it to the right by #4# to give us #y = sqrt (x-4)#

graph{y = sqrt(x-4}

Now we can stretch the graph by a factor of #2# by multiplying the equation by #2#: #y = 2sqrt(x-4)#

graph{y = 2sqrt(x-4)}

And now we deal with the negative sign. This flips the graph across the #x#-axis

graph{y=-2sqrt(x-4)}

There we go! We took the parent graph, #sqrt(x)# and shifted it to the right #4# units, then we stretched the graph by a factor of #2#, and finally we flipped the graph across the #x#-axis.

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