Introduction to Practice graphing algebra:
A function is a relation between two items of a data algebraically expressed. A graph is a visual representation of a function.
It is always easier to perceive the nature of a function visually rather than working out the algebraic equations. This is the reason why we see graphs in almost all the establishments which describe the performance, conveys the key information etc.
Practice Graphing Algebra-uses
Use of Graphing Functions and Straight lines
For example, the following graph depicts the total sales of a company for a period of past few years.
From the graph one can immediately conclude that the company is almost steadily increasing its sale. Attention is also drawn that in the year 2004 – 2005, there has been a drop in the sales and the concerned persons of the company can look into the reasons. The same information could also given by algebraic functions, part by part but that would not have been a help for drawing immediate conclusions.
My forthcoming post is on Exponential and Logarithmic Functions, Radical Equations Examples will give you more understanding about Algebra.
However, although the graph of a function gives a visual representation and ready information, the algebraic function is no less important. Unless the relation is worked out algebraically it will not be possible to make a graph. For example each year’s sale must have been algebraically worked out from the available data, a simple plot is made and the graph is drawn by interpolation and extrapolation.
Practice Graphing Algebra-inferences
Inferences from Graphing Functions and Straight lines
The graph shows the nature of functions. If it is a straight line, the function is linear, if the graph is a parabola, the function is quadratic etc. The graphs of various types of functions are shown below.
A relation can not be function if a particular domain coreesponds to more than one range. This can be easily identified in a graph.
If any portion of the graph of a relation is vertical, then the relation is not a function.
Method of Graphing Functions and Straight lines
To graph a straight line, that is a linear function just two points are sufficient. Plot two points on a grid with the help of an input-output relation. Draw a straight line passing through these two points.
Although two points are sufficient to draw the graph of a linear equation, you may be more comfortable by plotting additional points from an input-output table of the function.
For drawing graphs of other type of functions, first you need to identify the type of function.
The nature of a function will give an idea how to determine the key points. The key points must be plotted first.
Make an input-output table for more number of values and plot them on the grid. The more the number of points you gather, it will be easier to draw the graph. Join the points by a smooth curve remembering the possible shapes of the graphs of the function.
Example problems on Graphing Functions and Straight lines
Example 1
The graph of the function y = x – 4 will be
A) a straight line
B) a parabola
C) exists only in 1st and 2nd quadrants
D) exists only in 1st and 4th quadrants
Solution
A) A straight line is the graph of a linear function. The given function is also a linear function.
B) A parabola is the graph of a quadratic function. The given function is a linear function and not a quadratic function
C) The graph which exists only in 1st and 2nd quadrants represents a exponential function. But the given function is linear and not exponential.
D) The graph which exists only in 1st and 4th quadrants represents a logarithmic function. But the given function is linear and not logarithmic.
Therefore, the correct choice is A.
Example 2
The above graph represents
A) an exponential function
B) a logarithmic function
C) a quadratic function
D) a linear function
Solution
A) The graph of an exponential function exists only in 1st and 2nd quadrants. But the given graph is a parabola occupying all the quadrants.
B) The graph of a logarithmic function exists only in 1st and 4th quadrants. But the given graph is a parabola occupying all the quadrants.
C) The graph of a quadratic function is a parabola and the given graph is also a parabola
D) The graph of a linear function is a straight line. But the given graph is a parabola.
Therefore, the correct choice is C.
A function is a relation between two items of a data algebraically expressed. A graph is a visual representation of a function.
It is always easier to perceive the nature of a function visually rather than working out the algebraic equations. This is the reason why we see graphs in almost all the establishments which describe the performance, conveys the key information etc.
Practice Graphing Algebra-uses
Use of Graphing Functions and Straight lines
For example, the following graph depicts the total sales of a company for a period of past few years.
My forthcoming post is on Exponential and Logarithmic Functions, Radical Equations Examples will give you more understanding about Algebra.
However, although the graph of a function gives a visual representation and ready information, the algebraic function is no less important. Unless the relation is worked out algebraically it will not be possible to make a graph. For example each year’s sale must have been algebraically worked out from the available data, a simple plot is made and the graph is drawn by interpolation and extrapolation.
Practice Graphing Algebra-inferences
Inferences from Graphing Functions and Straight lines
The graph shows the nature of functions. If it is a straight line, the function is linear, if the graph is a parabola, the function is quadratic etc. The graphs of various types of functions are shown below.
A relation can not be function if a particular domain coreesponds to more than one range. This can be easily identified in a graph.
If any portion of the graph of a relation is vertical, then the relation is not a function.
Method of Graphing Functions and Straight lines
To graph a straight line, that is a linear function just two points are sufficient. Plot two points on a grid with the help of an input-output relation. Draw a straight line passing through these two points.
Although two points are sufficient to draw the graph of a linear equation, you may be more comfortable by plotting additional points from an input-output table of the function.
For drawing graphs of other type of functions, first you need to identify the type of function.
The nature of a function will give an idea how to determine the key points. The key points must be plotted first.
Make an input-output table for more number of values and plot them on the grid. The more the number of points you gather, it will be easier to draw the graph. Join the points by a smooth curve remembering the possible shapes of the graphs of the function.
Example problems on Graphing Functions and Straight lines
Example 1
The graph of the function y = x – 4 will be
A) a straight line
B) a parabola
C) exists only in 1st and 2nd quadrants
D) exists only in 1st and 4th quadrants
Solution
A) A straight line is the graph of a linear function. The given function is also a linear function.
B) A parabola is the graph of a quadratic function. The given function is a linear function and not a quadratic function
C) The graph which exists only in 1st and 2nd quadrants represents a exponential function. But the given function is linear and not exponential.
D) The graph which exists only in 1st and 4th quadrants represents a logarithmic function. But the given function is linear and not logarithmic.
Therefore, the correct choice is A.
Example 2
The above graph represents
A) an exponential function
B) a logarithmic function
C) a quadratic function
D) a linear function
Solution
A) The graph of an exponential function exists only in 1st and 2nd quadrants. But the given graph is a parabola occupying all the quadrants.
B) The graph of a logarithmic function exists only in 1st and 4th quadrants. But the given graph is a parabola occupying all the quadrants.
C) The graph of a quadratic function is a parabola and the given graph is also a parabola
D) The graph of a linear function is a straight line. But the given graph is a parabola.
Therefore, the correct choice is C.
