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.
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.
Example 1. Draw graph :
y = ex
y = ex+ 1
y = ex – 1
1. y = ex
We know that
y = ex is an exponential function & it is plotted like as—
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 —
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 —
Example 2. Draw graph —
- y = | x |
- y = | x | + 1
- y = | x | – 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
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
