When you want to draw a coordinate graph for the simple functions, reach this page. Here you will learn the complete details about graphs of simple functions quickly and with fewer efforts. Generally, a function is a process or a relation that associates with the elements. You can check the examples of various basic functions and functions which are multiples of numbers.
Common Functions
The list of common functions and their graphs are provided below.
1. Linear Function:
It is a straight line and the function which is in the form of y = mx + c is called the linear function.
2. Square Function:
The function which is in the form of f(x) = x² is known as the square function.
3. Cube Function:
The function which is in the form of y = x³ is called the cube function.
4. Square Root Function:
If the function is in the form of y = √x, then it is called the square root function.
5. Absolute Value Function:
For every function we have positive and negative value possibilities i.e f(x) = I x I is called the absolute value function.
6. Logarithmic Function:
A function that has log in it is known as the logarithmic function.
7. Reciprocal Function:
A function that is in the form of fraction and numerator value is 1 is called the reciprocal function.
8. Exponential Function:
The function that has an exponent is called the exponential function.
9. Sine Function:
A function that includes trigonometric sine is called the sine function.
10. Cosine Function:
The function which contains trigonometric cosine is known as the cosine function.
11. Tangent Function:
A function that has trigonometric tan is called the tangent function.
Steps to Draw Graph of Function
- First of all, take some function.
- Find the values of x for the corresponding values of y. That means substitute random values of x to get the y values.
- Place those values in a table.
- Plot the obtained points on a graph paper.
- If you wanted the respective function value at a particular point, then figure it out from the graph.
Solved Example Questions
1. Draw the graph of the function y = 5x. From the graph, find the value of y, when x = 0.5, 0.2.
Solution:
Given function is y = 5x
For some different values of x, the corresponding values of y are given below.
| x | -1 | 0 | 1 |
|---|---|---|---|
| y = 5x | -5 | 0 | 5 |
Plot the points P (0, 0), Q (1, 5), R (-1, -5) on the graph paper and join those points to form a straight line.
Reading values from the graph of sample function y = 5x
On the x-axis, take the point L at x = 0.5.
Draw LB ⊥ x-axis, meeting the graph at B.
Clearly, AL = 2.5 units.
Therefore, x = 0.5 ⇒ y = 2.5.
Take a point M at x = 0.2
Draw MA ⊥ x-axis, meeting the graph at A.
MA = 1 unit
Therefore, x = 0.2 ⇒ y = 1
2. Draw the graph of the function y = 2x². From the graph, find the value of y, when x = -1.5, 0.5.
Solution:
Given function is y = 2x²
For some different values of x, the corresponding values of y are given below.
| x | -1 | 0 | 1 | 2 |
|---|---|---|---|---|
| y | 2 | 0 | 2 | 8 |
Plot the points A (-1, 2), B (0, 0), C (1, 2), D (2, 8) on a graph and join those points.
Reading values from the graph of sample function y = 2x²
On the x-axis, take the point L at x = -1.5.
Draw LP ⊥ x-axis, meeting the graph at A.
Clearly, PL = 4.5 units.
Therefore, x = -1.5 ⇒ y = 4.5.
Take a point M at x = 0.5
Draw MB ⊥ x-axis, meeting the graph at AB
MA = 0.5 unit
Therefore, x = 0.5 ⇒ y = 0.5
3. Draw the graph of the function p(n) = 3n – 1. From the graph, find the value of p(n), when n = 2, 1.5
Solution:
Given function is p(n) = 3n – 1
For some different values of x, the corresponding values of y are given below.
| n | -1 | 0 | 1 |
|---|---|---|---|
| p(n) = 3n – 1 | -4 | -1 | 2 |
Plot the points x (-1, -4), y (0, -1), z (1, 2) on the graph paper and join those points to form a straight line.
Reading values from the graph of sample function p(n) = 3n – 1
On the x-axis, take the point L at n = 2.
Draw LA ⊥ x-axis, meeting the graph at A.
Clearly, AL = 5 units.
Therefore, n = 2 ⇒ p(n) = 5
Take a point M at n = 1.5
Draw MB ⊥ x-axis, meeting the graph at B
MB = 3.5 units
Threrefore, 2 = 1.5 ⇒ p(n) = 3.5