Graph the following function using the technique of shifting, compressing, strecthing and/or reflecting
Find domain and range of the function
g(x)=2√x-3 + 7
One important thing to remember in these problems is that
we must shift vertically UP or DOWN last.
We start with
y = √x
Its domain is [0,
)
Its range is [0,)
Then we stretch it vertically by a factor of 2 by multiplying
the right side by 2 and we get
y = 2√x
Its domain is [0,)
Its range is [0,)
Note that these did not change on this step
Then we shift it horizontally to the right by 3 units by
replacing x by (x-3) in the right side and we get:
y = 2√x-3
Its domain is now [3,)
Its range is [0,)
Note that the domain shifted 3 to the right but
the range did not change on this step.
Then finally we shift it vertically up by 7 units by adding 7
to the right side.:
y = 2√x-3 + 7
And that is the graph of
g(x) = 2√x-3 + 7
Its domain is [3,)
Its range is [7,)
Note that the domain did not change from the previous step,
but the range shifted 7 units upward.
Edwin
