Graphs of Common Functions
Maths: Edexcel IGCSE Higher, topic 3.4.1
Common Functions
To sketch a graph, see if it is linear, quadratic or cubic. Then plot some x and y co-ordinates and join them up in the right shape.
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Linear
- Linear functions are straight lines in the form y = mx + c.
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Quadratic
- Quadratic functions have an x2 term.
- They are in the form y = ax2 + bx + c.
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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.
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 co-ordinates and join them up in the right shape.
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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 in the bottom left and then has a steep gradient up to the top right.
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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.
Trigonometric Functions
To sketch trigonometric graphs (y = sin(x), y = cos(x), y = tan(x)) use x values which are multiples of 90° since these are the important points on the graph.
Tangent
- tan(x) repeats every 180°
- There are vertical lines at 90°, 270°, ... because the function is undefined at these points.
sin(x)
- sin(x) repeats every 360°.
sin(x) and cos(x)
- cos(x) also repeats every 360°.
- They have the same wave shape but the cosine graph is shifted by 90° compared to the sine graph.
Test yourself on Graphs of Common Functions
What type of graph is this?
What type of graph is this?
What type of graph is this?
Is y = 2x3 + x2 + 4x - 6 cubic, quadratic or linear?
Is y = 3x2 + 4x - 6 cubic, quadratic or linear?