Find any points of discontinuity for the rational function.

1. (x + 6)(x + 2)(x + 8)
y = _____________________
(x + 9)(x + 7)

2. x - 8
y = _____________________
x^2 + 6x - 7

The first function is discontinuous when x = -9 and when x = -7

The second is discontinuous when x = -7 and when x = 1

There are no "points" of discontinuity, the curves approach an asymptote, not points.

Find the

point of discontinuity of the function
F(x) =𝒙
𝟐−𝟑𝒙+𝟐
𝒙
𝟐 −𝟓𝒙+𝟔

To find the points of discontinuity for the given rational functions, we need to determine where the denominator becomes zero since dividing by zero is undefined.

For the first rational function, y = (x + 6)(x + 2)(x + 8) / (x + 9)(x + 7).

To find the points of discontinuity, we set the denominator equal to zero and solve for x:

(x + 9)(x + 7) = 0

Let's solve for x:

x + 9 = 0 or x + 7 = 0

x = -9 or x = -7

Therefore, the points of discontinuity for the first rational function are x = -9 and x = -7.

Now let's move on to the second rational function, y = (x - 8) / (x^2 + 6x - 7).

We need to find where the denominator (x^2 + 6x - 7) becomes zero.

To find the points of discontinuity, we set the denominator equal to zero and solve for x:

x^2 + 6x - 7 = 0

Let's solve for x:

We can use factoring or the quadratic formula to solve this equation.

Using factoring:

(x + 7)(x - 1) = 0

x + 7 = 0 or x - 1 = 0

x = -7 or x = 1

Therefore, the points of discontinuity for the second rational function are x = -7 and x = 1.

To find the points of discontinuity for a rational function, you need to identify the values of x that make the denominator equal to zero. These values are called the points of discontinuity, as they would cause the function to be undefined.

Let's find the points of discontinuity for the given rational functions:

1. The points of discontinuity for the first rational function, (x + 6)(x + 2)(x + 8) / (x + 9)(x + 7), are the values of x that make the denominators (x + 9) and (x + 7) equal to zero.

Setting (x + 9) = 0, we find:
x = -9

Setting (x + 7) = 0, we find:
x = -7

Therefore, the points of discontinuity for the first rational function are x = -9 and x = -7.

2. For the second rational function, x - 8 / (x^2 + 6x - 7), let's find the points of discontinuity using the same method.

Setting the denominator (x^2 + 6x - 7) equal to zero, we can solve the quadratic equation:
x^2 + 6x - 7 = 0

Using factoring or the quadratic formula, we find:
(x + 7)(x - 1) = 0

Setting (x + 7) = 0, we find:
x = -7

Setting (x - 1) = 0, we find:
x = 1

Therefore, the points of discontinuity for the second rational function are x = -7 and x = 1.

Remember that these points of discontinuity represent values of x where the rational function is not defined.