fill in the following table for values of x near 3. what do you observe about the value of f(x) as x…

fill in the following table for values of x near 3. what do you observe about the value of f(x) as x approaches 3 from the right? from the left? f(x)=\\frac{1}{x - 3}\n\n| x | 2.9 | 2.99 | 2.999 | 3.001 | 3.01 | 3.1 |\n| ---- | ---- | ---- | ---- | ---- | ---- | ---- |\n| f(x) | | | | | | |\n\nas x approaches 3 from the left, f(x) approaches. select an answer\nas x approaches 3 from the right, f(x) approaches. select an answer\n\nquestion help: video ebook written example

fill in the following table for values of x near 3. what do you observe about the value of f(x) as x approaches 3 from the right? from the left? f(x)=\\frac{1}{x - 3}\n\n| x | 2.9 | 2.99 | 2.999 | 3.001 | 3.01 | 3.1 |\n| ---- | ---- | ---- | ---- | ---- | ---- | ---- |\n| f(x) | | | | | | |\n\nas x approaches 3 from the left, f(x) approaches. select an answer\nas x approaches 3 from the right, f(x) approaches. select an answer\n\nquestion help: video ebook written example

Answer

Explanation:

Step1: Substitute x - values into function

For (x = 2.9), (f(2.9)=\frac{1}{2.9 - 3}=\frac{1}{- 0.1}=-10). For (x = 2.99), (f(2.99)=\frac{1}{2.99 - 3}=\frac{1}{-0.01}=-100). For (x = 2.999), (f(2.999)=\frac{1}{2.999 - 3}=\frac{1}{-0.001}=-1000). For (x = 3.001), (f(3.001)=\frac{1}{3.001 - 3}=\frac{1}{0.001}=1000). For (x = 3.01), (f(3.01)=\frac{1}{3.01 - 3}=\frac{1}{0.01}=100). For (x = 3.1), (f(3.1)=\frac{1}{3.1 - 3}=\frac{1}{0.1}=10).

Answer:

(x) (f(x))
(2.9) (- 10)
(2.99) (-100)
(2.999) (-1000)
(3.001) (1000)
(3.01) (100)
(3.1) (10)

As (x) approaches (3) from the left ((x<3)), (f(x)) approaches (-\infty). As (x) approaches (3) from the right ((x > 3)), (f(x)) approaches (\infty).