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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
The only place where this graph cuts either axis is at (0, 0).

3 Sketching the graph Step 2: Find the vertical asymptotes
The denominator is zero when x = -2 or x = 3 The vertical asymptotes are x = -2

4 Sketching the graph Step 2: Find the vertical asymptotes
The denominator is zero when x = -2 or x = 3 The vertical asymptotes are x = -2 and x = 3

5 Sketching the graph Step 2: Find the vertical asymptotes
The denominator is zero when x = -2 or x = 3 The vertical asymptotes are x = -2 and x = 3 For now, don’t worry about the behaviour of the graph near the asymptotes. You may not need this information.

6 Sketching the graph Step 3: Examine the behaviour as x tends to infinity For numerically large values of x, y → 0. For large positive values of x, all three of x, (x + 2) and (x – 3) are positive, so y is positive. As x → ∞, y → 0 from above.

7 Sketching the graph Step 3: Examine the behaviour as x tends to infinity For numerically large values of x, y → 0. For large positive values of x, all three of x, (x + 2) and (x – 3) are positive, so y is positive. As x → ∞, y → 0 from above.

8 Sketching the graph Step 3: Examine the behaviour as x tends to infinity For numerically large values of x, y → 0. For large negative values of x, all three of x, (x + 2) and (x – 3) are negative, so y is negative. As x → -∞, y → 0 from below.

9 Sketching the graph Step 3: Examine the behaviour as x tends to infinity For numerically large values of x, y → 0. For large negative values of x, all three of x, (x + 2) and (x – 3) are negative, so y is negative. As x → -∞, y → 0 from below.

10 Sketching the graph Step 4: Complete the sketch
Since the graph only crosses the x axis at the origin, we can complete the part of the graph to the right of x = 3

11 Sketching the graph Step 4: Complete the sketch
Since the graph only crosses the x axis at the origin, we can complete the part of the graph to the right of x = 3 and to the left of x = -2

12 Sketching the graph Step 4: Complete the sketch
Since the graph only crosses the x axis at the origin, we can complete the part of the graph to the right of x = 3 and to the left of x = -2

13 Sketching the graph Step 4: Complete the sketch
Now there is a difficulty. We know that the graph goes through the origin, but we don’t know whether it goes from positive to negative or negative to positive. Try a value of x between -2 and 0. You should find that y is positive in this case.

14 Sketching the graph Step 4: Complete the sketch
Now there is a difficulty. We know that the graph goes through the origin, but we don’t know whether it goes from positive to negative or negative to positive. Try a value of x between -2 and 0. You should find that y is positive in this case.

15 Sketching the graph Step 4: Complete the sketch
Now there is a difficulty. We know that the graph goes through the origin, but we don’t know whether it goes from positive to negative or negative to positive. Try a value of x between 0 and 3. You should find that y is negative in this case.

16 Sketching the graph Step 4: Complete the sketch
Now there is a difficulty. We know that the graph goes through the origin, but we don’t know whether it goes from positive to negative or negative to positive. Try a value of x between 0 and 3. You should find that y is negative in this case.

17 Sketching the graph Step 4: Complete the sketch
The sketch can now be completed.

18 Sketching the graph Step 4: Complete the sketch
The sketch can now be completed.


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