Introduction for step function graph:
If the function of any two quantities can be represented by means of a straight line in a graph paper then such graphs are known as linear straight function. In the previous class we learnt about “Time-Distance” graph under linear graphs. Now let us learn some more linear graphs.
However, since quadratics have curvy lines (called ‘Parabola’) rather than straight lines generated by linear function, there are some additional considerations to graph it.
For graphing a straight line, two points are sufficient, though we generally plot three or more points to be on safer side. But to graph a quadratic, three points will not be sufficient. Depending upon the extension of the curve, the points may be
increased.
For each value of x the function y = ax2 + bx + c gives the corresponding value of y and we obtain the ordered pairs (x, y) of real numbers. The set of all such ordered pairs which defines the graph y = ax2 + bx + c is called quadratic graph.
Step of Linear Function Graph:
Quantity-Cost graph
We know that in a direct variation if one variable increases then the other variable also increases and if one variable decreases then the other variable also decreases.
Let the cost of 1 pen be $.20. Then the cost of 4 pens is $ 80. the cost of 10 pens is $.200, the cost of 20 pens is $.400.
So, on It is easily understood that if the number of pens increases then the cost also increases Similarly if the number of pens decreases then the cost also decreases.
Hence we understand that quantity and cost are in direct variation. As we mentioned earlier the relation between quantity and cost can be shown in at function of graph by taking quantity along the X-axis and cost along the Y-axis. The graph obtained is a straight line. This graph is known as “Quantity-Cost “graph.
Example:
From the given data draw a linear graph showing the relationship between quantity and cost of linear function y = 10x.
Quantity (In numbers) X
1 2 3 4 5 6 7 8
Cost (In $) Y
10 20 30 40 50 60 70 80
Solution:
Step 1: Conversions, the given table of function can be converted as points (I, 10), (2, 20) , (3, 30), (4, 40), (5, 50), (6, 60), (7, 70), (8, 80).
Step 2: Identifications, all these points lie in the first quadrant only since both the X-coordinates and Y-coordinates are positive.
Step 3: As shown in figure draw the X-axis and Y-axis .
Step 4: Mark 1, 2, 3 ...8 along the X-axis at every centimeter and mark 10, 20, 30 ...80 along the Y-axis at every centimeter.
Step 5: Plot the points (1, 10), (2, 20), (3, 30), (4, 40), (5, 50), (6, 60), (7, 70) and (8, 80) in the graph paper. Join the points. We get (a straight line function. This graph shows the function between quantity and cost.
If the function of any two quantities can be represented by means of a straight line in a graph paper then such graphs are known as linear straight function. In the previous class we learnt about “Time-Distance” graph under linear graphs. Now let us learn some more linear graphs.
However, since quadratics have curvy lines (called ‘Parabola’) rather than straight lines generated by linear function, there are some additional considerations to graph it.
For graphing a straight line, two points are sufficient, though we generally plot three or more points to be on safer side. But to graph a quadratic, three points will not be sufficient. Depending upon the extension of the curve, the points may be
increased.
For each value of x the function y = ax2 + bx + c gives the corresponding value of y and we obtain the ordered pairs (x, y) of real numbers. The set of all such ordered pairs which defines the graph y = ax2 + bx + c is called quadratic graph.
Step of Linear Function Graph:
Quantity-Cost graph
We know that in a direct variation if one variable increases then the other variable also increases and if one variable decreases then the other variable also decreases.
Let the cost of 1 pen be $.20. Then the cost of 4 pens is $ 80. the cost of 10 pens is $.200, the cost of 20 pens is $.400.
So, on It is easily understood that if the number of pens increases then the cost also increases Similarly if the number of pens decreases then the cost also decreases.
Hence we understand that quantity and cost are in direct variation. As we mentioned earlier the relation between quantity and cost can be shown in at function of graph by taking quantity along the X-axis and cost along the Y-axis. The graph obtained is a straight line. This graph is known as “Quantity-Cost “graph.
Example:
From the given data draw a linear graph showing the relationship between quantity and cost of linear function y = 10x.
Quantity (In numbers) X
1 2 3 4 5 6 7 8
Cost (In $) Y
10 20 30 40 50 60 70 80
Solution:
Step 1: Conversions, the given table of function can be converted as points (I, 10), (2, 20) , (3, 30), (4, 40), (5, 50), (6, 60), (7, 70), (8, 80).
Step 2: Identifications, all these points lie in the first quadrant only since both the X-coordinates and Y-coordinates are positive.
Step 3: As shown in figure draw the X-axis and Y-axis .
Step 4: Mark 1, 2, 3 ...8 along the X-axis at every centimeter and mark 10, 20, 30 ...80 along the Y-axis at every centimeter.
Step 5: Plot the points (1, 10), (2, 20), (3, 30), (4, 40), (5, 50), (6, 60), (7, 70) and (8, 80) in the graph paper. Join the points. We get (a straight line function. This graph shows the function between quantity and cost.
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