**Shifting Graph Up and Down Examples :**

Here we are going to see some examples to learn how to shift the graph up or down.

**Shifting a graph up or down :**

Suppose f is a function and a > 0. Define functions g and h by

g(x) = f(x) + a and h(x) = f(x) − a.

Then,

- The graph of g is obtained by shifting the graph of f up a units
- The graph of h is obtained by shifting the graph of f down a units.
- g and h have the same domain as f
- The range of g is obtained by adding a to every number in the range of f ;
- The range of h is obtained by subtracting a from every number in the range of f ;

**Question 1 :**

Define a function g by

g(x) = f(x) + 1,

where f is the function defined by f(x) = x^{2}, 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.

**Solution :**

(a) Here g(x) is defined precisely defined by f(x). In other words, the domain of g equals the domain of f. Thus the domain of g is the interval [−1, 1].

(b) To find the range of g, we have to apply the values that we find the domain of g.

By adding every number with the of f, we may find the range of g.

f(x) = x^{2}

If x = -1, then y = 1

If x = 0, then y = 0

If x = 1, then y = 1

Range of f is [0, 1]. By adding 1 to every values, we get the range of the function g(x) is [1, 2].

(c) g(x) = x^{2} + 1

Here 1 is added with the function, so we have to move the graph of the function 1 unit up.

**Question 2 :**

Define a function h by h(x) = f(x) − 1, where f is the function defined by f(x) = x^{2}, with the domain of f the interval [−1, 1].

(a) Find the domain of h.

(b) Find the range of h.

(c) Sketch the graph of h.

**Solution :**

(a) Here h(x) is defined precisely defined by f(x). In other words, the domain of f equals the domain of f. Thus the domain of h is the interval [−1, 1].

(b) To find the range of h, we have to apply the values that we find the domain of f.

f(x) = x^{2}

If x = -1, then y = 1

If x = 0, then y = 0

If x = 1, then y = 1

Then range of the function h(x) is [0, 1].By subtracting 1 from every values, we get the range of the function h(x) that is [-1, 0].

(c) h(x) = x^{2} - 1

Here 1 is subtracted from the function, so we have to move the graph of the function 1 unit .

**Question 3 :**

Assume that f is the function defined on the interval [1, 2] by the formula f(x) = 4 / x^{2}. 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.

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).

**Solution :**

(a) By shifting the given graph, 1 unit up we get the graph of g.

(b) The domain of g is the same as the domain of f . Thus the domain of g is the interval [1, 2].

(c) Because the graph of g is obtained by shifting the graph of f up 1 unit, we have g(x) = f(x) + 1. Thus

g(x) = (4/x^{2}) + 1

for each number x in the interval [1, 2].

(d) The range of g is obtained by adding 1 to each number in the range of f . Thus the range of g is the interval [2, 5].

After having gone through the stuff given above, we hope that the students would have understood "Shifting Graph Up and Down Examples".

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**