Drawing the graph of the reciprocal function

1. Drawing the graph of the reciprocal function

2. = - - 2 y ( x 2 ) 1 . 5 1 = y - - 2 ( x 2 ) 1 . 5 Y Whenever the original function is 0 the reciprocal will be undefined so we need asymptotes where the graph crosses the x-axis Whenever the original function is +1 or –1 the reciprocal will be also be +1 or –1 so we can put points on the original graph where the y-co-ord is +1 or –1. Also the vertex is at (2, – 1.5) so the “vertex” of the reciprocal will be at (2, – 0.67) If x > 3.2 For the original: x + y  + For the reciprocal: x +  y  + 0 For the original: x 3.2then y  + 0 For the reciprocal: x 3.2y  +  If x < 0.8 For the original: x –  y  + For the reciprocal: x –  y  + 0 For the original: x 0.8then y  + 0 For the reciprocal: x 0.8y  +  10 5 If 0.8 < x < 3.2 For the original: x 0.8then y  – 0 For the reciprocal: x 0.8then y  – For the original: x 3.2then y  – 0 For the reciprocal: x 3.2then y  – X -2 -1 1 2 3 4 5 -5 -10

3. Your turn … This time you explain why the graph of the reciprocal looks the way that it does!

4. = - - 2 y ( x 2 ) 1 . 5 1 = y - - 2 ( x 2 ) 1 . 5 Y 10 5 X -2 -1 1 2 3 4 5 -5 -10