Example of a Graph
Equation: y = mx+b
Description: A straight line graph where m is the slope (steepness) of the line, and b is the yintercept (where the line crosses the yaxis).
Equation: y = ax^{2 }+ bx + c
Description: Quadratic graphs are graphs of a quadratic function and can be recognized as they include a squared term.
The shape of a quadratic graph is a parabola.
The graphs have one tuning point – a minimum point or a maximum point.
Cubic graphs are graphs of a cubic function and can be recognized as they include a cubed term.
E.g. An x^{3} term.
The graphs often have two turning points – a minimum point and a maximum point.
Exponential graphs are graphs of an exponential function and can be recognized as they include a kx term where k is the base and x is the exponent (power). The graphs can be a growth curve when k is greater than 1 or a decay curve when k is less than 1.
Reciprocal graphs are graphs of a reciprocal function and can be recognized as they include a 1/x term.
They are of the form:
x^{2} + y^{2} = r^{2}
where r^{2} is the radius of the circle.
Example 1: Match the graph with its equation
Equation 1: y = 2^{x}
Equation 2: y = x^{2 }+ x  2
Equation 3: x^{2 }+ y^{2 }= 4
Equation 4: y = x^{3} x  2
Sol:
Graph A has 2 vertices; it is very likely to be a cubic function.
Equation 4 is a cubic function with a yintercept at −2 which is at the end of the equation when x=0
Graph B is a growth curve so its equation will have a term with x as an exponent (power); equation 1 has a term with x as an exponent.
There is a parabola graph, so this is the graph of a quadratic function that has a x^{2} term. Graph C is Equation 2
There is a circle graph. It has a center (0,0) and radius 2^{2 }; so its equation would be:
x^{2}+y^{2}=2^{2}
Graph D is Equation 3
Example 2: Recognise the types of graphs:
Equation 1: x+y=5
Equation 2: y=5/x
Equation 3: x^{2}+y^{2}=25
Equation 4: y=0.5^{x}
Sol:
There is a straight line graph so this is the graph of a linear function that has no visible powers. There is no parabola graph so there is no quadratic function.
Graph B is Equation 1
There is a circle graph. It has a center (0,0) so its equation would be:
x^{2}+y^{2}=r^{2}
Graph A is Equation 3
Graph C is not a growth curve but it is a decay curve so its equation will have a term with x as an exponent (power). Equation 4 has a term with x as an exponent.
Graph D is a curve in which 1/x has 2 sections in different quadrants of the coordinate grid. It is likely to be a reciprocal graph with a term. Equation 2 has a term with x as a denominator of a fraction.
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1. What is a graph and how is it related to physics? 
2. What are the different types of graphs used in physics? 
3. How can graphs be used to analyze motion in physics? 
4. How do graphs help in understanding scientific experiments in physics? 
5. What are the advantages of using graphs in physics? 
335 videos845 docs218 tests

Concept of Angle and TRatios Doc  2 pages 
Logarithm: Concepts with Examples Doc  6 pages 
Log Functions Video  20:04 min 

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