2.5.5
Graphs of Common Functions 1
Common Functions
Common Functions
To sketch a graph, see if it is linear, quadratic or cubic. Then plot some x and y coordinates and join them up in the right shape.
![Illustrative background for Linear](https://image-v2.cdn.app.senecalearning.com/2018-03/78971726-7a9d-488b-9b53-36dede1341d5/desmos-graph%20(20),h_400,q_80,w_640.png)
![Illustrative background for Linear ?? "content](https://image-v2.cdn.app.senecalearning.com/2018-03/78971726-7a9d-488b-9b53-36dede1341d5/desmos-graph%20(20),h_400,q_80,w_640.png)
Linear
Linear
- Linear functions are straight lines in the form y = mx + c.
![Illustrative background for Quadratic](https://image-v2.cdn.app.senecalearning.com/2018-03/c730cc09-83dd-4456-8e51-684062621aca/desmos-graph%20(21),h_400,q_80,w_640.png)
![Illustrative background for Quadratic ?? "content](https://image-v2.cdn.app.senecalearning.com/2018-03/c730cc09-83dd-4456-8e51-684062621aca/desmos-graph%20(21),h_400,q_80,w_640.png)
Quadratic
Quadratic
- Quadratic functions have an x2 term.
- They are in the form y = ax2 + bx + c.
![Illustrative background for Cubic](https://image-v2.cdn.app.senecalearning.com/2018-03/6d48067f-ef94-4b27-9d48-2c0e7948315e/desmos-graph%20(23),h_400,q_80,w_640.png)
![Illustrative background for Cubic ?? "content](https://image-v2.cdn.app.senecalearning.com/2018-03/6d48067f-ef94-4b27-9d48-2c0e7948315e/desmos-graph%20(23),h_400,q_80,w_640.png)
Cubic
Cubic
- Cubic functions are in the form y = ax3 + bx2 + cx + d.
- If a > 0, it starts in the bottom left and goes up to the right.
- If a < 0, it starts in the top left and goes down to the right.
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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