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 givengraph 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 isan exponential function & it is plottedlike as—
2. y = ex+ 1
f(x) —> f(x) +a , when f(x) is given
Heref(x) = ex
To drawy = ex + 1,
+1 unit upward shifting
So , graphlook like as —
3.y = ex – 1
f(x) —> f(x) – a , when f(x) is given
Here f(x) = ex
To drawy = 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| isan modulus function & it can plottedlikeas—