2.5.6
Graphs of Common Functions 2
Common Functions
Common Functions
To sketch a graph, look at whether it is exponential, reciprocal or some other type of graph. Then plot some x and y coordinates and join them up in the right shape.
![Illustrative background for Exponential](https://image-v2.cdn.app.senecalearning.com/2018-03/4dcdb8d0-8f8b-43a8-a703-e51958ebad72/desmos-graph%20(25),h_400,q_80,w_640.png)
![Illustrative background for Exponential ?? "content](https://image-v2.cdn.app.senecalearning.com/2018-03/4dcdb8d0-8f8b-43a8-a703-e51958ebad72/desmos-graph%20(25),h_400,q_80,w_640.png)
Exponential
Exponential
- Exponential functions are of the form y = kx or y = k-x.
- They are completely above the x-axis and go through the point (0, 1).
- If k > 1 and the power is positive then the graph starts at the bottom left and then has a steep gradient up to the top right.
![Illustrative background for Reciprocal](https://image-v2.cdn.app.senecalearning.com/2018-03/a6645dce-5d6e-4167-b175-f6ebd1ad02ae/desmos-graph%20(26),h_400,q_80,w_640.png)
![Illustrative background for Reciprocal ?? "content](https://image-v2.cdn.app.senecalearning.com/2018-03/a6645dce-5d6e-4167-b175-f6ebd1ad02ae/desmos-graph%20(26),h_400,q_80,w_640.png)
Reciprocal
Reciprocal
- Reciprocal graphs never cross the x or y axis. They are only in 2 parts (quadrants) of the graph.
- They are usually y = a⁄x or xy = a.
1Proof
1.1Types of Numbers
1.2Notation
2Algebra & Functions
2.1Powers & Roots
2.2Quadratic Equations
2.3Inequalities
2.4Polynomials
2.5Graphs
2.7Transformation of Graphs
3Coordinate Geometry
3.1Straight Lines
3.2Circles
3.2.1Equations of Circles centred at Origin
3.2.2Finding the Centre & Radius
3.2.3Equation of a Tangent
3.2.4Circle Theorems - Perpendicular Bisector
3.2.5Circle Theorems - Angle at the Centre
3.2.6Circle Theorems - Angle at a Semi-Circle
3.2.7Equation of a Perpendicular Bisector
3.2.8Equation of a Circumcircle
3.2.9Circumcircle of a Right-angled Triangle
3.3Parametric Equations (A2 only)
4Sequences & Series
4.1Binomial Expansion
5Trigonometry
5.2Trigonometric Functions
5.3Triangle Rules
6Exponentials & Logarithms
6.1Exponentials & Logarithms
7Differentiation
7.1Derivatives
7.2Graphs & Differentiation
7.3Differentiation With Trigonometry and Exponentials
7.4Rules of Differetiation (A2 only)
7.5Parametric & Implicit Differentiation
8Integration
8.1Integration
9Numerical Methods
9.1Finding Solutions
9.2Finding the Area
10Vectors
10.12D Vectors
10.23D Vectors
10.3Vector Proofs
Jump to other topics
1Proof
1.1Types of Numbers
1.2Notation
2Algebra & Functions
2.1Powers & Roots
2.2Quadratic Equations
2.3Inequalities
2.4Polynomials
2.5Graphs
2.7Transformation of Graphs
3Coordinate Geometry
3.1Straight Lines
3.2Circles
3.2.1Equations of Circles centred at Origin
3.2.2Finding the Centre & Radius
3.2.3Equation of a Tangent
3.2.4Circle Theorems - Perpendicular Bisector
3.2.5Circle Theorems - Angle at the Centre
3.2.6Circle Theorems - Angle at a Semi-Circle
3.2.7Equation of a Perpendicular Bisector
3.2.8Equation of a Circumcircle
3.2.9Circumcircle of a Right-angled Triangle
3.3Parametric Equations (A2 only)
4Sequences & Series
4.1Binomial Expansion
5Trigonometry
5.2Trigonometric Functions
5.3Triangle Rules
6Exponentials & Logarithms
6.1Exponentials & Logarithms
7Differentiation
7.1Derivatives
7.2Graphs & Differentiation
7.3Differentiation With Trigonometry and Exponentials
7.4Rules of Differetiation (A2 only)
7.5Parametric & Implicit Differentiation
8Integration
8.1Integration
9Numerical Methods
9.1Finding Solutions
9.2Finding the Area
10Vectors
10.12D Vectors
10.23D Vectors
10.3Vector Proofs
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