Graph f(x) to f(x) ± a

Graph : f(x) -> f(x) ± a

In mathematics  , Graph is pictorial representation of data or values in an organized manner.

In graph , the point in ordered in the graph related to another point. So , actually points on the graph related to each other.

We are advised to student to study this section carefully ,because it gives a very short approaches to various lengthy problem in competitive examination.

Transformation :

1 .       f(x) to f(x) ± a , when f(x) is given

Where  ‘a’ is positive constant.

1.1     f(x) —>  f(x) + a

Here ‘a’ upward shifting in f(x).

So , shift the given graph of f(x)  ‘a’  unit upward.

f(x) to f(x)+a

1.2     f(x) —>  f(x) – a

Here ‘a’ downward shifting in f(x).

So , shift the given  graph of f(x)  ‘a’  unit downward.

f(x) to f(x) - a

Example 1. Draw graph :

    1. y = ex
    2. y = ex+ 1
    3. y = ex – 1
1.  y = ex

We know that

y = ex  is  an exponential function & it is plotted  like as—

draw graph y = ex

2. y = ex+ 1

 

f(x) —> f(x) +a , when f(x) is given

Here f(x) = ex

To draw  y = ex + 1  , 

+1 unit upward shifting

So , graph  look like as —

draw graph y=ex+1

3.  y = ex – 1

f(x) —> f(x) – a , when f(x) is given

Here f(x) = ex

To draw  y = ex – 1  , 

– 1 unit downward shifting

So , graph is look like as —

draw graph y=ex-1

Example 2.  Draw graph —

    1.   y = | x |
    2. y  = | x | + 1
    3. y  = | x | – 1
    1.   y = | x |

We know that

y = |x|   is  an modulus function & it can plotted  like  as—

y = | x | = -x  for x <0

y = | x | =  x  for x > 0

draw graph y=|x|

2.  y = |x| + 1

 

f(x) —> f(x) +a , when f(x) is given

Here f(x) =  | x |

 

To draw  y =  |x |+ 1  ,  1 unit upward shifting

So , graph  look like as —

y = | x | + 1  = -x + 1 , for x <0

y = | x | + 1  =  x + 1 , for x > 0

  3.  y = |x| – 1

 

f(x) —> f(x) – a , when f(x) is given

Here f(x) = |x|

To draw  y = |x| – 1  ,  1 unit downward shifting

So , graph  look like as —

y = | x | + 1  = -x – 1 , for x <0

y = | x | + 1  =  x – 1 , for x > 0

draw graph y=|x|-1