Question

Determine the intercepts of the line. yy y y -intercept: (\Big( ( left parenthesis ,, , comma )\Big) ) right parenthesis xx x x -intercept: (\Big( ( left parenthesis ,, , comma )\Big) ) right parenthesis

Answer 1

Question:

Give all the x and y intercept of the function

$f(x) = \frac{3x^2 - 3x-60}{2x^3 + 2x^2-34x+30}$

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;

$f(x) = \frac{3x^2 - 3x-60}{2x^3 + 2x^2-34x+30} =\frac{3(x-5)(x+4)}{2x^3 + 2x^2-34x+30}$

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.