Answer:
domain: all real numbers except 2 and -10; x-intercept: 4; y-intercept: 1/5
Step-by-step explanation:
The domain consists of the set of all possible values x can be. In a fraction, the denominator cannot be equal to 0. We can solve for the values x cannot be equal to by factoring and exclude them out of the domain once we’ve found them:
To factor x^2 + 8x - 20, we are looking for two numbers that have a product of -20 and a sum of 8. These two numbers are 10 and -2. So, it can be factored to:
(x + 10)(x -2) not equal 0
So x ≠ 2 and x ≠ -10.
To find the x-intercept, the value of y would be zero. We can substitute y as 0 to get:
0 = (x - 4) / x^2 + 8x - 20
The only way for this fraction to equal 0, is for the numerator to be 0. We get the equation:
x - 4 = 0,
And x = 4
To find the y-intercept, the value of x would be 0. We can substitute x with 0 to get:
y = -4 / -20 = 1/5
These answers align with the second option.
