Question

For the function q(x)=(x^2+6x+8) / (x+4) , at each of the following values of x, select whether q(x) has a zero, a vertical asymptote, or a removable discontinuity.

A) x = −4: Zero
B) x = −4: Vertical Asymptote
C) x = −4: Removable Discontinuity
D) x = −2: Zero
E) x = −2: Vertical Asymptote
F) x = −2: Removable Discontinuity

Answer 1

For the function q(x)=(x^2+6x+8) / (x+4), q(x) has a zero at x = -4 and x = -2, and it has a vertical asymptote at x = -4 and x = -2, as well as a removable discontinuity at x = -4 and x = -2.

Step-by-step explanation:

For the function q(x)=(x^2+6x+8) / (x+4), we can determine whether q(x) has a zero, a vertical asymptote, or a removable discontinuity at each value of x.

A) For x = -4, we substitute x = -4 into the function to find q(x) = 0. Therefore, q(x) has a zero at x = -4.

B) For x = -4, we substitute x = -4 into the denominator of the function, which results in division by zero. Therefore, q(x) has a vertical asymptote at x = -4.

C) For x = -4, we substitute x = -4 into the function and simplify to get q(x) = 2. Therefore, q(x) has a removable discontinuity at x = -4.

D) For x = -2, we substitute x = -2 into the function to find q(x) = 0. Therefore, q(x) has a zero at x = -2.

E) For x = -2, we substitute x = -2 into the denominator of the function, which results in division by zero. Therefore, q(x) has a vertical asymptote at x = -2.

F) For x = -2, we substitute x = -2 into the function and simplify to get q(x) = 4. Therefore, q(x) has a removable discontinuity at x = -2.