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Learn all the What, Why, & How about Different Types of Graphs

Mathematical data with two or more variables can be expressed diagrammatically through the use of graphs. Find out more about them with Tutoreye.

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“Graphs” is an easy and scoring section in the exams, and something that you can use a good deal in your future PowerPoint Presentations:
 

  • What is a Graph?
  • Bar Graph
  • Line Graph
  • Histogram
  • Pie Chart
  • Venn Diagram
  • Box & Whisker Chart
  • Pictographs
  • Exponential Graphs
  • Logarithmic Graphs
  • Trigonometric Graphs
  • Frequency Distribution Graphs

 

Graphs Frequently Asked Questions:

Question 1: If f and g are the functions whose graphs are shown, let ux=f(x)g(x) and v(x) = f(x)/g(x)


Graph
 

  • Find u'(1)
  • Find v'(5)

 

Explanation: To find the derivative of the function u(x) and v(x), we can use the product rule and the quotient rule of the derivative respectively.
 

  • Find u'(1)

So, if ux=f(x)g(x). 

Then, we know that u'x=f'xgx+g'xf(x)

After analyzing the graph, we can see that: f(1)=3, f'(1)=3. And, g(1)=2, g'(1) = -1.

So, u'(1)=f'(1)g(1)+g'(1)f(1)

Let us plug the values.

u'1=3×2+-1×3=6-3 = 3

So, u'1=3
 

  • Find v'(5)

We have given v(x) = f(x)/g(x).

Then, using the quotient rule, 

v'x=gxf'x-fxg'x/(g(x))^2

Looking at the graph, we have: f(5)=2, f'(5)=-1/4. And, g(5)=2, g'(5)=1.

Now, let us plug these values.

v'5=g(5)f'(5)-f(5)g'(5)/g(5)^2

v'5=2×(-1/4)-2×1/(1)^2= (-1/2)-2/1=-5/2

Hence, v'5=-5/2

 

Question 2: Which graphs represent an object moving in the positive direction?

An object moves in the positive direction if its velocity is positive. The direction of motion cannot be stated by analyzing the slope of the velocity-time graph.

Example:


Graph 1
 

Question 3: Which graphs represent an object moving in the negative direction?

The direction of an object would be negative if it has a negative velocity. The direction of motion cannot be defined by the slope of the velocity-time graph.


The positive or negative slope of the velocity-time graph does not state the positive or negative direction. It just describes how velocity is changing with respect to time.

Example:
 

Graph 2

 

Graph 3

 

 

 

 

 

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