Complete the table of inputs and outputs for the given function.
[tex]g(x)=3-8 x[/tex]
| x | g(x) |
|---|---|
| | 0 |
| 0 | |
| | -5 |
| 3 | |
Answer (1)
Find x when g ( x ) = 0 : Solve 3 − 8 x = 0 to get x = 8 3 .
Find g ( x ) when x = 0 : Evaluate g ( 0 ) = 3 − 8 ( 0 ) = 3 .
Find x when g ( x ) = − 5 : Solve 3 − 8 x = − 5 to get x = 1 .
Find g ( x ) when x = 3 : Evaluate g ( 3 ) = 3 − 8 ( 3 ) = − 21 .
The completed table values are 8 3 , 3 , 1 , − 21 .
Explanation
Understanding the Problem We are given the function g ( x ) = 3 − 8 x and a table with x and g ( x ) values. We need to find the missing values in the table.
Finding x when g(x) = 0 First, we need to find the value of x when g ( x ) = 0 . So we set up the equation 3 − 8 x = 0 and solve for x . Adding 8 x to both sides gives 3 = 8 x . Dividing both sides by 8, we get x = 8 3 .
Finding g(x) when x = 0 Next, we need to find the value of g ( x ) when x = 0 . We substitute x = 0 into the function: g ( 0 ) = 3 − 8 ( 0 ) = 3 − 0 = 3 .
Finding x when g(x) = -5 Now, we need to find the value of x when g ( x ) = − 5 . We set up the equation 3 − 8 x = − 5 and solve for x . Subtracting 3 from both sides gives − 8 x = − 8 . Dividing both sides by -8, we get x = 1 .
Finding g(x) when x = 3 Finally, we need to find the value of g ( x ) when x = 3 . We substitute x = 3 into the function: g ( 3 ) = 3 − 8 ( 3 ) = 3 − 24 = − 21 .
Final Answer So, the completed table is:
x
g(x)
3/8
0
0
3
1
-5
3
-21
The answers are 8 3 , 3 , 1 , and − 21 .
Examples
Linear functions like g ( x ) = 3 − 8 x are used to model various real-world scenarios. For example, if you are losing weight at a rate of 8 pounds per week but started at 3 pounds overweight, g ( x ) represents your weight relative to your ideal weight after x weeks. Understanding how to evaluate and solve for inputs and outputs of such functions can help you predict and manage your weight loss progress.
