Mathematics Exam – Graphs and Functions

Mathematics Examination

Graphs and Functions – Unit #10 | Class 9th (SNC)

Unit #10: Graphs and Functions

MATHEMATICS EXAMINATION PAPER

Subject: Mathematics (SNC) – Graphs and Functions
Class: 9th
Date: ______________
Time Allowed: ______________
Total Marks: ______________
Candidate Name:
Roll Number:
Marks Obtained:

Q1. Choose the correct option. (10 × 1 = 10 marks)

Q2. Write down short answers of following questions. (15 × 2 = 30 marks)

1Plot the graph of the following function: y = 3⁻ˣ from x = -2 to x = 4

Sketch your graph in the space above. Label axes and key points.

2Plot the graph of the following function: y = \(\frac{2}{x}\), x ≠ 0

Sketch your graph in the space above. Show asymptotes.

3Plot the graph of following for x from -5 to 5: y = 15 – x²

Sketch your graph in the space above. Show vertex and intercepts.

4Define Quadratic Function. Write its general form.

5Define Cubic Function. Write its general form.

6Define Reciprocal Function. Write its general form.

7If y = x³ + 2x² – 5x – 6 where -3.5 ≤ x ≤ 2.5, then draw the graph of the cubic function.

Sketch your graph in the space above. Show intercepts and turning points.

8Find the value of y in y = 4x² if -5 ≤ x ≤ 5. Draw input and output values table also tell the type of function.

Create a table with x and y values: \[ \begin{array}{c|c} x & y = 4x² \\ \hline -5 & \\ -4 & \\ -3 & \\ -2 & \\ -1 & \\ 0 & \\ 1 & \\ 2 & \\ 3 & \\ 4 & \\ 5 & \\ \end{array} \]

9Sketch the graph of the following linear function: y = 3x – 5

Sketch your graph in the space above. Show slope and intercepts.

10Sketch the graph of the following linear function: y = -2x + 8

Sketch your graph in the space above. Show slope and intercepts.

11Plot the graph of the following quadratic function: y = x² + x – 2

Sketch your graph in the space above. Show vertex and intercepts.

12Plot the graph of the following function: y = \(\frac{1}{x-3}\), x ≠ 3

Sketch your graph in the space above. Show asymptotes.

13Plot the graph of the following function: y = x1/3 (cube root function)

Sketch your graph in the space above.

14Plot the graph of the following function: y = 3x1/3

Sketch your graph in the space above.

15Plot the graph of the following function: y = 2x⁻² (or y = \(\frac{2}{x²}\))

Sketch your graph in the space above. Show asymptotes.

Q3. Write detailed answers of the following questions. (Answer any 2) (2 × 5 = 10 marks)

1. Supply and Demand Functions

The supply and demand functions for a particular market are given by the equations:

\[ P_s = Q^2 + 5 \quad \text{and} \quad P_d = Q^2 – 10Q, \] where P represents price and Q represents quantity.

Sketch the graph of each function over the interval Q = -20 to Q = 20.

2. Comparison of Functions

Plot the graphs of y = x² and y = x³ on the same diagram. (Example 2)

3. Reciprocal Function Graph

Sketch the graph of the following reciprocal function:

\[ y = \frac{1}{x-0.5}, \quad x \neq 0.5 \]

(Example 6)