Question:
Give all the x and y intercept of the function
[tex]f(x) = \frac{3x^2 - 3x-60}{2x^3 + 2x^2-34x+30}[/tex]
Answer:
The x intercepts are x = 5 and x = -4
The y intercept is at y = -2
Step-by-step explanation:
Factorizing the numerator of the expression we find the x intercepts as follows;
[tex]f(x) = \frac{3x^2 - 3x-60}{2x^3 + 2x^2-34x+30} =\frac{3(x-5)(x+4)}{2x^3 + 2x^2-34x+30}[/tex]
Therefore, the x intercept are
x = 5 and x = -4
To find the y intercept, we put x = 0 to get y = -2
Therefore, the y intercept is at y = -2
Factorizing the denominator we find the values for which the equation is undefined
2·x³ + 2·x² - 34·x + 30 = 2·(x-1)·(x-3)·(x+5) which gives
x = 1, 3 and -5.
