Question

make a function table for each function. then state the domain and range of the function. example 2 4. $f(x) = 6x - 4$ 5 $f(x) = 5 - 2x$ 6. $f(x) = 7 + 3x$

Explanation:

Step1: Choose x-values

Let's pick x = 0, 1, 2, 3 for simplicity.

Step2: Calculate f(x) for x=0

Substitute x = 0 into \( f(x) = 5 - 2x \): \( f(0) = 5 - 2(0) = 5 \)

Step3: Calculate f(x) for x=1

Substitute x = 1: \( f(1) = 5 - 2(1) = 3 \)

Step4: Calculate f(x) for x=2

Substitute x = 2: \( f(2) = 5 - 2(2) = 1 \)

Step5: Calculate f(x) for x=3

Substitute x = 3: \( f(3) = 5 - 2(3) = -1 \)

Step6: Determine Domain

For linear functions \( f(x) = mx + b \), the domain is all real numbers (\( \mathbb{R} \)) since there are no restrictions on x.

Step7: Determine Range

Since it's a linear function with \( m
eq 0 \), the range is also all real numbers (\( \mathbb{R} \)) as y can take any real value.

Function Table:

x	5 - 2x	f(x)
1	5 - 2	3
2	5 - 4	1
3	5 - 6	-1

Domain and Range:

Domain: All real numbers (\( \mathbb{R} \))
Range: All real numbers (\( \mathbb{R} \))

Answer:

Step1: Choose x-values

Let's pick x = 0, 1, 2, 3 for simplicity.

Step2: Calculate f(x) for x=0

Substitute x = 0 into \( f(x) = 5 - 2x \): \( f(0) = 5 - 2(0) = 5 \)

Step3: Calculate f(x) for x=1

Substitute x = 1: \( f(1) = 5 - 2(1) = 3 \)

Step4: Calculate f(x) for x=2

Substitute x = 2: \( f(2) = 5 - 2(2) = 1 \)

Step5: Calculate f(x) for x=3

Substitute x = 3: \( f(3) = 5 - 2(3) = -1 \)

Step6: Determine Domain

For linear functions \( f(x) = mx + b \), the domain is all real numbers (\( \mathbb{R} \)) since there are no restrictions on x.

Step7: Determine Range

Since it's a linear function with \( m
eq 0 \), the range is also all real numbers (\( \mathbb{R} \)) as y can take any real value.

Function Table:

x	5 - 2x	f(x)
1	5 - 2	3
2	5 - 4	1
3	5 - 6	-1

Domain and Range:

Domain: All real numbers (\( \mathbb{R} \))
Range: All real numbers (\( \mathbb{R} \))