Find the indicated intercept(s) of the graph of the function.?

Question

y intercept of= 13x/6x+8

x intercept= x^2-7x-30/x^3-64

Answer 1

Let f(x) = 13x / (6x + 8).

To find the y - intercept, plug in x = 0

f(0) = 13(0) / (6(0) + 8)

f(0) = 0 / (0 + 8)

f(0) = 0

So when x = 0, we have y = 0

So this means that the y-intercept is (0, 0)

 

x intercept= (x² - 7x - 30) / (x³-64)

Let f(x) = (x² - 7x - 30) / (x³-64)

To find the x - intercept, f(x) = 0

(x² - 7x - 30) / (x³-64) = 0

Multiply each side by (x³-64).

(x² - 7x - 30) = 0

Now solve the equation using factor method.

x² - 10x + 3x - 30 = 0

x(x - 10) + 3(x - 10) = 0

Take out common factors.

(x - 10)(x + 3) = 0

x - 10 = 0 or x + 3 = 0.

x - 10 = 0

Add 10 to each side.

x = 10

And x + 3 = 0

Subtract 3 from each side.

x = -3

So the x-intercepts are (10, 0) and (-3, 0).