QuestionJuly 15, 2025

Consider the following function: f(x)=(-5x+9)/(x+2) Step 2 of 2:What type of discontinuity is at the discontinuous point? Answer 2 Points Choose the correct answer from the options below. Removable Discontinuity Non-Removable Discontinuity Jump Discontinuity

Consider the following function: f(x)=(-5x+9)/(x+2) Step 2 of 2:What type of discontinuity is at the discontinuous point? Answer 2 Points Choose the correct answer from the options below. Removable Discontinuity Non-Removable Discontinuity Jump Discontinuity
Consider the following function:
f(x)=(-5x+9)/(x+2)
Step 2 of 2:What type of discontinuity is at the discontinuous point?
Answer 2 Points
Choose the correct answer from the options below.
Removable Discontinuity
Non-Removable Discontinuity
Jump Discontinuity

Solution
4.0(234 votes)

Answer

Non-Removable Discontinuity Explanation 1. Identify the discontinuous point The function f(x)=\frac {-5x+9}{x+2} is discontinuous where the denominator is zero. Set x+2=0, so x=-2. 2. Determine type of discontinuity Check if the numerator also becomes zero at x=-2. Substitute x=-2 into -5x+9: -5(-2)+9=10+9=19 \neq 0. Since the numerator is not zero, the discontinuity is non-removable.

Explanation

1. Identify the discontinuous point<br /> The function $f(x)=\frac {-5x+9}{x+2}$ is discontinuous where the denominator is zero. Set $x+2=0$, so $x=-2$.<br /><br />2. Determine type of discontinuity<br /> Check if the numerator also becomes zero at $x=-2$. Substitute $x=-2$ into $-5x+9$: $-5(-2)+9=10+9=19 \neq 0$. Since the numerator is not zero, the discontinuity is non-removable.
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