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Curve sketching This PowerPoint presentation shows the different stages involved in sketching the graph.

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Presentation on theme: "Curve sketching This PowerPoint presentation shows the different stages involved in sketching the graph."— Presentation transcript:

1 Curve sketching This PowerPoint presentation shows the different stages involved in sketching the graph

2 Sketching the graph Step 1: Find where the graph cuts the axes
When x = 0, y = 4/3, so the graph goes through the point (0, 4/3). y ≠ 0 for any values of x, so the graph does not cut the x axis.

3 Sketching the graph Step 2: Find the vertical asymptotes
The denominator is not zero for any real values of x, so there are no vertical asymptotes.

4 Sketching the graph Step 3: Examine the behaviour as x tends to infinity For numerically large values of x, y → 1. So y = 1 is a horizontal asymptote.

5 Sketching the graph Step 3: Examine the behaviour as x tends to infinity For numerically large values of x, y → 0. So y = 1 is a horizontal asymptote. For large positive values of x, y is slightly greater than 1. As x → ∞, y → 1 from above.

6 Sketching the graph Step 3: Examine the behaviour as x tends to infinity For numerically large values of x, y → 0. So y = 1 is a horizontal asymptote. For large positive values of x, y is slightly greater than 1. As x → ∞, y → 1 from above.

7 Sketching the graph Step 3: Examine the behaviour as x tends to infinity For numerically large values of x, y → 0. So y = 1 is a horizontal asymptote. For large negative values of x, y is slightly less than 1. As x → -∞, y → 1 from below.

8 Sketching the graph Step 3: Examine the behaviour as x tends to infinity For numerically large values of x, y → 0. So y = 1 is a horizontal asymptote. For large negative values of x, y is slightly less than 1. As x → -∞, y → 1 from below.

9 Sketching the graph Step 4: Complete the sketch
We can now complete the sketch.

10 Sketching the graph Step 4: Complete the sketch
We can now complete the sketch. We can’t be sure exactly where the turning points are, but this does not matter in a sketch graph.


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