How do you describe the transformation of #f(x)=sqrt(1/2x)-4# from a common function that occurs and sketch the graph?

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Answer 1 · 2017-10-01T15:11:19

We can write the given equation:

# f(x)=sqrt(1/2x) -4 #

In the form:

# (f(x)+4) = sqrt(x/2) #

We should now recognise this as the graph of the function

# y=sqrt(x) #

graph{sqrt(x) [-5, 10, -8, 8]}

Which is:

1) scaled by a factor of #1/2# in the #x#-direction to give #y=sqrt(x/2)#
graph{sqrt(x/2) [-5, 10, -8, 8]}

2) translated #4# units down to give #(y+4)=sqrt(x/2)#
graph{sqrt(x)-4 [-5, 10, -8, 8]}