Question

Identify whether each value of x is a discontinuity of the function by typing asymptote, hole, or neither.

5x
x3 + 5x2 + 6x
x= -3
x = -2
x=0
x = 2
x= 3
x=5
DONE

Answer 1

To determine whether each value of x is a discontinuity of the function, we analyze the function to find asymptotes or holes. For the given function, x = -2 and x = -3 are asymptotes, x = 0 is a hole, and the remaining values of x do not create any discontinuities.

Step-by-step explanation:

To determine whether each value of x is a discontinuity of the function, we need to analyze the function and look for asymptotes or holes. Let's consider the function f(x) = (5x) / (x^3 + 5x^2 + 6x).

To identify asymptotes, we need to find the values of x where the denominator of the function is equal to zero. For x = -2 and x = -3, the denominator becomes zero, which indicates that there are vertical asymptotes at x = -2 and x = -3. These values are neither holes nor asymptotes.

For x = 0, the denominator also becomes zero, but the numerator is not zero. This indicates that there is a hole at x = 0.

For the remaining values of x (2, 3, and 5), neither the numerator nor the denominator becomes zero. Therefore, these values do not create either holes or asymptotes. So the answer is:

• x = -3: asymptote
• x = -2: asymptote
• x = 0: hole
• x = 2: neither
• x = 3: neither
• x = 5: neither

Answer 2

nobody gave the right answers but here it is :

Step-by-step explanation:

x = −3

⇒ asymptote

x = −2

⇒ asymptote

x = 0

⇒ hole

x = 2

⇒ neither

x = 3

⇒ neither

x = 5

⇒ neither