It is a powerpoint presentation that will help the students to enrich their knowledge about Senior High School subject of General Mathematics. It is comprised about Rational functions and its intercepts. It also includes some examples and exercises of the said topic.

1. INTERCEPTS OF A RATIONAL
FUNCTION
GENERAL MATHEMATICS

2. INTERCEPTS
It is the set of points where the graph of the rational
function intersects at the x and y axes respectively

3. x-INTERCEPTS
It is the set of points where the graph of the rational
function crosses the x-axis
Formula for X-Intercept:
Substitute 0 for y and solve for x

4. Y-INTERCEPTS
It is the set of points where the graph of the rational
function crosses the y-axis
Formula for Y-Intercept:
Substitute 0 for x and solve for y

5. EXAMPLES:
Find the intercepts of the function:
𝑓 𝑥 =
𝑥 + 8
𝑥 − 2

6. EXAMPLES:
Y-Intercept:
𝑓 0 =
𝑥 + 8
𝑥 − 2
𝑓 0 =
0 + 8
0 − 2
𝑓 0 =
8
−2
y = - 4

7. EXAMPLES:
X-Intercept:
0 =
𝑥+8
𝑥 −2
Substitute 0 for y or f(x)
0 = 𝑥 + 8 Multiply both sides by x – 2
x = -8

9. EXERCISE:
Find the intercepts (x and y) of the following functions.

10. ITEM NO. 1
Find the intercepts of the function:
𝑓 𝑥 =
𝑥2
− 5𝑥 + 6
𝑥2 − 2𝑥 + 3

11. ITEM NO. 2
Find the intercepts of the function:
𝑓 𝑥 =
𝑥2
+ 9
𝑥2 − 3

12. ITEM NO. 3
Find the intercepts of the function:
𝑓 𝑥 =
𝑥 − 6
𝑥2 − 36

13. ITEM NO. 4
Find the intercepts of the function:
𝑓 𝑥 =
𝑥2
− 5𝑥 + 4
𝑥2 − 4𝑥 − 5

14. ITEM NO. 5
Find the intercepts of the function:
𝑓 𝑥 =
3
𝑥 − 1

15. ITEM NO. 6
Find the intercepts of the function:
𝑓 𝑥 =
𝑥 − 1
2𝑥 + 1

16. ITEM NO. 7
Find the intercepts of the function:
𝑦 =
𝑥2
− 2
𝑥 + 2

17. ITEM NO. 8
Find the intercepts of the function:
𝑦 =
3𝑥
(𝑥 + 2)2