The equations of the transformed graphs are [tex]f(x) = \frac 23\sqrt{x - 3}[/tex], [tex]f(x) = 8\sqrt{x }-3[/tex], [tex]f(x) = \sqrt{\frac x7} + 5[/tex] and [tex]f(x) = \sqrt{-x} - 10[/tex]
The function #1
The function is given as::
[tex]f(x) = \sqrt{x}[/tex]
It is shifted right by 3 units.
So, we have:
[tex]f(x) = \sqrt{x - 3}[/tex]
It is shrunk vertically by a factor of 2/3
[tex]f(x) = \frac 23\sqrt{x - 3}[/tex]
Hence, the equation of the transformed graph is [tex]f(x) = \frac 23\sqrt{x - 3}[/tex]
The function #2
The function is given as::
[tex]f(x) = \sqrt{x}[/tex]
It is stretched vertically by a factor of 8
[tex]f(x) = 8\sqrt{x }[/tex]
It is shifted down by 3 units.
So, we have:
[tex]f(x) = 8\sqrt{x }-3[/tex]
Hence, the equation of the transformed graph is [tex]f(x) = 8\sqrt{x }-3[/tex]
The function #3
The function is given as::
[tex]f(x) = \sqrt{x}[/tex]
It is stretched horizontally by a factor of 7
[tex]f(x) = \sqrt{\frac x7}[/tex]
It is shifted up by 5 units.
So, we have:
[tex]f(x) = \sqrt{\frac x7} + 5[/tex]
Hence, the equation of the transformed graph is [tex]f(x) = \sqrt{\frac x7} + 5[/tex]
The function #4
The function is given as::
[tex]f(x) = \sqrt{x}[/tex]
It is reflected across the y-axis
[tex]f(x) = \sqrt{-x}[/tex]
It is shifted down by 10 units.
So, we have:
[tex]f(x) = \sqrt{-x} - 10[/tex]
Hence, the equation of the transformed graph is [tex]f(x) = \sqrt{-x} - 10[/tex]
Read more about function transformation at:
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