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.