Graphs of Reciprocals

Size: px

Start display at page:

Download "Graphs of Reciprocals"

Oscar Alexander
5 years ago
Views:

1 Graphs of Reciprocals The reciprocal of a number is divided by that number So the reciprocal of 3 is 3 5 The reciprocal of is 5 5 The only number that cannot have a reciprocal is 0 Dividing by zero is not possible (Why) We can also talk about the reciprocals of mathematical functions: The reciprocal of the function is, the reciprocal of ( + 5 ) is + 5 etc Use autograph to draw the line y 0 Think about the reciprocal function, y 0 a) (i) For what value of is the value of ( 0 ) zero (ii) What will happen to 0 at this value b) As, 0 What will happen to 0 c) As, 0 What will happen to 0 d) On Paper, try to sketch the graph y See how accurate you were by drawing 0 the graph y in autograph; you will have to enter the equation y/(-0) 0 You can see that the curve breaks at the value 5 This is because can t take the value 5 in the equation of the curve, since it leads to division by zero The curve can t cross this vertical line, and it tends to on either side of it The line 5 is said to be an ASYMPTOTE of the curve y 0

2 Use autograph to draw the curve y + Now think about the reciprocal function, y + a) Is + ever zero Will there be any values for which curve have any ASYMPTOTES + doesn t eist Will the b) As, + What will happen to + c) As, + What will happen to + d) On Paper, try to sketch the graph y See how accurate you were by drawing the + graph y + in autograph; you will have to enter the equation y/( +) e) What do you notice about the turning points of y + and its reciprocal, y + 3 Use autograph to draw the curve y 4 Think about its reciprocal, y 4 a) Is 4 ever zero Will there be any values for which doesn t eist What will 4 happen to the curve y 4 at these values Will it have any ASYMPTOTES b) As ±, 4 ± What will happen to 4 ± c) As from below, what will happen to d) As from above, what will happen to 4 4 e) On Paper, try to sketch the graph y See how accurate you were by drawing the 4 graph y 4 in autograph; you will have to enter the equation y/( -4) f) What do you notice about the turning points of y 4 and its reciprocal, y 4

3 4 Use autograph to draw the curve y + Think about its reciprocal, y + a) Is + ever zero Will there be any values for which will happen to the graph y + at these values + doesn t eist What b) On Paper, try to sketch the graph y the graph y + in Autograph See how accurate you were by drawing + c) What do you notice about the turning points of y + and its reciprocal, y + 5 Use autograph to draw the curve y + 4 Think about its reciprocal, y + 4 a) Is + 4 ever zero Will there be any values for which + 4 doesn t eist b) How could you have predicted that the curve ASYMPTOTES (Hint quadratic formula!) y + 4 would not have any c) On Paper, try to sketch the graph y See how accurate you were by + 4 drawing the graph y in Autograph + 4 d) What do you notice about the turning points of y + 4 and its reciprocal, y Without drawing any graphs, which of the following reciprocal curves will not feature any ymptotes y y y

4 7 Here is the graph of a function, though you are not told what the function is a) On Paper, try to sketch what the reciprocal of this function will look like b) The curve you are given in this question is in fact the graph y 3 9 Use Autograph to draw its reciprocal and see how accurate your sketch in part (a) w

8 Use Autograph to draw the curve y The reciprocal curve is y, or y a) Are there any values for which b) As ±, what happened to is zero c) As ±, what will happen to d) On Paper, try to sketch the

5 8 Use Autograph to draw the curve y The reciprocal curve is y, or y a) Are there any values for which b) As ±, what happened to is zero c) As ±, what will happen to d) On Paper, try to sketch the curve y Use Autograph to draw y, and see how accurate you were 9 a) Use algebra to solve the equation b) On Paper, sketch the curve y + 6 c) On Paper, attempt to sketch the curve y + 6 d) Use Autograph to determine the accuracy of your sketch in (c) 0 You are going to investigate the trigonometric curves a) Ensure that Autograph s unit of angle meurement is set to Radians Open a new D Graph Page and the appropriate icon in the upper toolbar should be selected shown b) Edit the default aes settings: in the menu select Aes >> Edit Aes and change the and y ranges to be those shown in the snapshot below: by setting the range to be you are effectively setting it to be π π

Accept all the other defaults and click OK c) Now enter the equation y sin You should see the waveform below: d) What do you think the graph y sin will look like Where will it break What will be its

6 Accept all the other defaults and click OK c) Now enter the equation y sin You should see the waveform below: d) What do you think the graph y sin will look like Where will it break What will be its maimum and minimum values On Paper, attempt to sketch this curve e) Open a new D graph page and set up the and y ranges you did in part (b) Draw the curve y sin How does your sketch compare Zoom out to see what the curve does on a larger range of values

Repeat Q7 for the curve y cos Investigate the reciprocal of y tan When drawing y tan you will have to set the and y ranges shown below: a) Draw the graph y tan b) What happens to tan when π c) What

7 Repeat Q7 for the curve y cos Investigate the reciprocal of y tan When drawing y tan you will have to set the and y ranges shown below: a) Draw the graph y tan b) What happens to tan when π c) What will happen to tan π when d) When is tan zero What will happen to tan at these values e) On Paper, attempt to sketch y tan f) Open a new D graph page and set up the and y ranges you did at the start of this question Draw the curve y tan How does your sketch compare Zoom out to see what the curve does for a larger range of values of Well done You have investigated a large number of curves and their reciprocals The ide involved here will be very important in the first few weeks of the C4 course in September

5.1 Graphing Sine and Cosine Functions.notebook. Chapter 5: Trigonometric Functions and Graphs

Chapter 5: Trigonometric Functions and Graphs 1 Chapter 5 5.1 Graphing Sine and Cosine Functions Pages 222 237 Complete the following table using your calculator. Round answers to the nearest tenth. 2