Question

complete the table of values for the function \\( f(x) = \frac{1}{x} \\).

\\( x \\)	\\( f(x) \\)		\\( x \\)	\\( f(x) \\)		\\( a = \square \\)
-0.1	b		0.01	f		\\( c = \square \\)
-0.01	c		0.1	g		\\( d = \square \\)
-0.001	d		1	h		\\( e = \square \\)
						\\( f = \square \\)

Explanation:

Step1: Find \( a \) (x = -1)

Substitute \( x = -1 \) into \( f(x) = \frac{1}{x} \). So \( f(-1) = \frac{1}{-1} = -1 \). Thus, \( a = -1 \).

Step2: Find \( b \) (x = -0.1)

Substitute \( x = -0.1 \) into \( f(x) = \frac{1}{x} \). \( f(-0.1) = \frac{1}{-0.1} = -10 \). So \( b = -10 \).

Step3: Find \( c \) (x = -0.01)

Substitute \( x = -0.01 \) into \( f(x) = \frac{1}{x} \). \( f(-0.01) = \frac{1}{-0.01} = -100 \). Thus, \( c = -100 \).

Step4: Find \( d \) (x = -0.001)

Substitute \( x = -0.001 \) into \( f(x) = \frac{1}{x} \). \( f(-0.001) = \frac{1}{-0.001} = -1000 \). So \( d = -1000 \).

Step5: Find \( e \) (x = 0.001)

Substitute \( x = 0.001 \) into \( f(x) = \frac{1}{x} \). \( f(0.001) = \frac{1}{0.001} = 1000 \). Thus, \( e = 1000 \).

Step6: Find \( f \) (x = 0.01)

Substitute \( x = 0.01 \) into \( f(x) = \frac{1}{x} \). \( f(0.01) = \frac{1}{0.01} = 100 \). So \( f = 100 \).

Answer:

\( a = -1 \)
\( b = -10 \)
\( c = -100 \)
\( d = -1000 \)
\( e = 1000 \)
\( f = 100 \)