Shifting the Graph Right or Left Examples :
Here we are going to see some examples of shifting the graph right or left.
The procedure for shifting the graph of a function to the right is illustrated by the following example:
Question 1 :
Define a function g by g(x) = f(x − 1), where f is the function defined by f(x) = x2, with the domain of f the interval [−1, 1].
(a) Find the domain of g.
(b) Find the range of g.
(c) Sketch the graph of g.
(a) Here the function g(x) is defined precisely when f(x − 1) is defined. The domain of the function f(x) is [-1, 1]. By adding 1 with coordinates, we will get domain of g(x).
[-1+1, 1+1] ==> [0, 2]
(b) The range of f is [0, 1], we see that the values taken on by g are the same as the values taken on by f . Thus the range of g equals the range of f , which is the interval [0, 1].
(c) Sketch the graph of g(x) = (x - 1)2
Since 1 is subtracted from x, we have to move the graph 1 unit to the right side.
Question 2 :
Assume that f is the function defined on the interval [1, 2] by the formula f(x) = 4 / x2 . Thus the domain of f is the interval [1, 2], the range of f is the interval [1, 4], and the graph of f is shown here.
The graph of g is obtained by shifting the graph of f left 3 units
For each function g described below:
(a) Sketch the graph of g.
(b) Find the domain of g (the endpoints of this interval should be shown on the horizontal axis of your sketch of the graph of g).
(c) Give a formula for g.
(d) Find the range of g (the endpoints of this interval should be shown on the vertical axis of your sketch of the graph of g).
Shifting the graph of f left 3 units gives this graph.
(b) The domain of g is obtained by subtracting 3 from every number in domain of f . Thus the domain of g is the interval [−2,−1].
(c) Because the graph of g is obtained by shifting the graph of f left 3 units, we have g(x) = f(x + 3). Thus g(x) = 4/(x + 3)2 for each number x in the interval [−2,−1].
(d) The range of g is the same as the range of f. Thus the range of g is the interval [1, 4].
After having gone through the stuff given above, we hope that the students would have understood "Shifting the Graph Right or Left Examples".
Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.
You can also visit our following web pages on different stuff in math.
APTITUDE TESTS ONLINE
ACT MATH ONLINE TEST
TRANSFORMATIONS OF FUNCTIONS
ORDER OF OPERATIONS
Customary units worksheet
Integers and absolute value worksheets
Nature of the roots of a quadratic equation worksheets
Point of intersection
MATH FOR KIDS
Word problems on linear equations
Trigonometry word problems
Word problems on mixed fractrions
Converting repeating decimals in to fractions