1. 28 – The Slant Asymptote No Calculator
Rational Function Investigations
28 – The Slant Asymptote No Calculator

2. Polynomial Division ReviewB E H K A D G J C F I L
Compute
Since dividing by 2x + 3,
place 2x + 3 in the first
column of your Area Model

3. Compute B E H K A D G J C F I L

4. is the remainder to the division.
Compute B E H K A D G J C F I L
What goes in Box G?
is the remainder to the division.
What goes in Box H?
What goes in Box I?
What goes in Box J?

5. Compute B F J A E I N C G K M D H L

6. Compute

7. Compute each division below:x –5
–5x 6 2 2x
–10 x 4 4x 6 –1 –x –4 x –1 –x
–10 2 2x –2

8. Compute each division below:x –2
–2x
–10 1 x 1 –1 –x x 4x 0x –1 –4
–4x

9. Slant Asymptote
If the degree of the numerator is EXACTLY one more than the degree of the denominator, the graph of the function will have a ‘slant asymptote’.
The equation of the slant asymptote is the result of ‘numerator divided by denominator’ (ignoring the remainder)
A function whose graph has a ‘slant asymptote’ will not have a horizontal asymptote.
The graph of f(x) will have a slant asymptote: y = x – 5.
The graph of f(x) will have a slant asymptote: y = x + 4.

10. The graph of f(x) will have a slant asymptote: y = x – 1.

11. horizontal intercepts [f(x) = 0]
–1, 4
vertical intercepts [x = 0]
vertical asymptote at x = –2
slant asymptote
y = x – 5
hole: none

12. horizontal intercepts [f(x) = 0]
–2, –1
vertical intercepts [x = 0]
vertical asymptote at x = 1
slant asymptote
y = x + 4
hole: none

13. horizontal intercepts [f(x) = 0]
–4, 3
vertical intercepts [x = 0]
vertical asymptote at x = –2
slant asymptote
y = x – 1
hole: none

14. horizontal intercepts [f(x) = 0]
–3, 4
vertical intercepts [x = 0]
vertical asymptote at x = –1
slant asymptote
y = x – 2
hole: none

15. horizontal intercepts [f(x) = 0]
vertical intercepts [x = 0]
vertical asymptote at x = 1
slant asymptote
y = x + 1
hole: none

16. horizontal intercepts [f(x) = 0]1
vertical intercepts [x = 0]
vertical asymptote at x = –2
vertical asymptote at x = 2
slant asymptote
y = x