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 = 3, so the graph goes through the point (0, 3).
When y = 0, there are no real 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 zero when x = -1
The vertical asymptote is x = -1

4. Sketching the graph Step 2: Find the vertical asymptotes
The denominator is zero when x = -1
The vertical asymptote is x = -1
For now, don’t worry about the behaviour of the graph near the asymptote. You may not need this information.

5. Sketching the graph
Step 3: Examine the behaviour as x tends to infinity
Dividing out gives
For numerically large values of x, y → x + 2.
This means that y = x + 2 is an oblique asymptote.

6. Sketching the graph
Step 3: Examine the behaviour as x tends to infinity
Dividing out gives
For numerically large values of x, y → x + 2.
This means that y = x + 2 is an oblique asymptote.

7. Sketching the graph
Step 3: Examine the behaviour as x tends to infinity
Dividing out gives
For numerically large values of x, y → x + 2.
This means that y = x + 2 is an oblique asymptote.
For large positive values of x, y is slightly greater than x + 2.
So as x → ∞, y → x + 2 from above.

8. Sketching the graph
Step 3: Examine the behaviour as x tends to infinity
Dividing out gives
For numerically large values of x, y → x + 2.
This means that y = x + 2 is an oblique asymptote.
For large negative values of x, y is slightly less than x + 2.
So as x → ∞, y → x + 2 from below.

9. Sketching the graph
Step 3: Examine the behaviour as x tends to infinity
Dividing out gives
For numerically large values of x, y → x + 2.
This means that y = x + 2 is an oblique asymptote.
For large negative values of x, y is slightly less than x + 2.
So as x → ∞, y → x + 2 from below.

10. Sketching the graph Step 4: Complete the sketch
It is easy to complete the part of the graph to the right of the asymptote, which must pass through the point on the y axis.

11. Sketching the graph Step 4: Complete the sketch
It is easy to complete the part of the graph to the right of the asymptote, which must pass through the point on the y axis.

12. Sketching the graph Step 4: Complete the sketch
We can also complete the part of the graph to the left of the asymptote, remembering that the graph does not cut the x-axis.

13. Sketching the graph Step 4: Complete the sketch
We can also complete the part of the graph to the left of the asymptote, remembering that the graph does not cut the x-axis.