In the xy-plane, the graph of function f, where , has exactly x-intercepts. One of these x-intercepts is . The rational function g is defined by . In the xy-plane, how many x-intercepts does the graph of have?
Enter a number or fraction, e.g. 5, 0.5, 1/2
Explanation
Question Type: Function Division (X-intercepts)
💡 Trick: Dividing by (x - 17) removes ONE x-intercept at x = 17 (becomes a hole).
Solution:
- f(x) has 8 x-intercepts, including (17, 0)
- g(x) = f(x)/(x - 17)
- At x = 17: f(17) = 0 and (x-17) = 0, creates a hole
- Other 7 x-intercepts remain
- Answer: 7
Answer: 7