Grade A Reciprocal Graphs Plot sketch and recognise

Grade A Reciprocal Graphs Plot, sketch and recognise graphs of reciprocal functions If you have any questions regarding these resources or come across any errors, please contact helpful-report@pixl. org. uk

Key Vocabulary Reciprocal Plot Graph Table Value Equation

What does a reciprocal graph look like? This is the graph of y = 1/x This is the graph of y = 5/x This is the graph of y = 10/x You can see above that for the equation y = a/x as you increase a the curve gets flatter and further away from the origin O.

How to plot a reciprocal graph? Complete the table values for y = 1/x + 2 x 0. 25 0. 5 1 2 3 4 y 6 4 3 5/2 7/3 9/4 What is y when x = 1? Substituting x = 1 into y = 1/x + 2 y = 1/1 + 2 y=1+2=3 y=3 What is y when x = 0. 5 Substituting x = 0. 5 into y = 1/x + 2 y = 1/0. 5 + 2 y=2+2=4 y=4

Now you try… 1) Complete the table values for y = 2/x x 0. 5 y 1 2 4 2 10 20 1/5 1/10 2) Complete the table values for y = 4/x + 1 x 0. 5 y 1 2 5 3 4 7/3 8 3/2 3) Complete the table values for y = 3/x + 2 x y 1/3 1 3 6 9 12 5/2 7/3 9/4

Now you try… 1) Complete the table values for y = 2/x x 0. 5 1 2 4 10 20 y 4 2 1 1/2 1/5 1/10 2) Complete the table values for y = 4/x + 1 x 0. 5 1 2 3 4 8 y 9 5 3 7/3 2 3/2 3) Complete the table values for y = 3/x + 2 x 1/3 1 3 6 9 12 y 11 5 3 5/2 7/3 9/4

Problem Solving and reasoning Complete the table values for y = 2/x x 0. 2 y 10 0. 4 0. 8 1 5/2 2 2 4

Problem Solving and reasoning Complete the table values for y = 2/x x 0. 2 0. 4 0. 8 1 2 4 y 10 5 5/2 2 1 1/2 There is no y value for when x = 0. 4. So substitute x = 0. 4 into the equation y = 2/x y = 2/0. 4 So y = 5 When x = 2 what is y? Substitute x = 2 into our equation y = 2/x. So y = 2/2 = 1 Therefore y = 1 when x = 2 Lastly what is y when x = 4? Substitute x = 4 into y = 2/x. y = 1/2 when x = 4

Problem Solving and reasoning Complete the table values for y = -4/x x -1 y 4 1 2 4 -1 8 12 -1/3

Problem Solving and reasoning Complete the table values for y = -4/x x -1 1 2 4 8 y 4 -4 -2 -1 -1/2 12 -1/3 What is the y value when x = 1? Substitute x = 1 into the equation y = -4/x y = -4/1 y = -4 What is the y value when x = 2? Substitute x = 2 into our equation y = -4/x. So y = -4/2 = -2 Therefore y = -2 when x = 2 Lastly what is y when x = 8? Substitute x = 8 into y = -4/x. y = -1/2 when x = 8

Reason and explain 1) What does the graph of y = -1/x look like? 2) What does the graph with equation y = 100/x look like in comparison to y = 1/x? True or false? For the equation y = 5/x + 1 When x = 10, y = 3/2? For the equation y = 22/x + 2 When x = 2, y = 1/2?