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**Unformatted text preview: **ng x + 2 = a gives x = a − 2 so that g (a − 2) =
f ((a − 2) + 2) = f (a) = b. As such, (a − 2, b) is on the graph of y = g (x). The point (a − 2, b) is
exactly 2 units to the left of the point (a, b) so the graph of y = g (x) is obtained by shifting the
graph y = f (x) to the left 2 units, as pictured below.
y y
(5, 5) (3, 5) 5 5 4 4 (2, 3)
(0, 3) 3 (4, 3) (2, 3) 2 2 (−2, 1) (0, 1)
−2 −1 1 2 3 4 5 x shift left 2 units 1 −2 −1 1 2 3 4 5 x −− − − − −→
−−−−−−
y = f (x) subtract 2 from each x-coordinate y = g (x) = f (x + 2) Note that while the ranges of f and g are the same, the domain of g is [−2, 3] whereas the domain
of f is [0, 5]. In general, when we shift the graph horizontally, the range will remain the same, but
the domain could change. If we set out to graph j (x) = f (x − 2), we would ﬁnd ourselves adding 1.8 Transformations 87 2 to all of the x values of the points on the graph of y = f (x) to eﬀect a shift to the right 2 units.
Generalizing, we have the following result.
Theo...

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