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Published byCorey Murphy Modified over 6 years ago
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Curve sketching This PowerPoint presentation shows the different stages involved in sketching the graph
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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Sketching the graph Step 4: Complete the sketch
We can now complete the sketch.
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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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