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The function g is defined by the following rule.

g (x) = -3x - 4
Complete the function table.
x g (x)
-2
0
1
3
4

11 answers

To complete the function table for \( g(x) = -3x - 4 \), we will calculate \( g(x) \) for each given value of \( x \).

  1. For \( x = -2 \): \[ g(-2) = -3(-2) - 4 = 6 - 4 = 2 \]

  2. For \( x = 0 \): \[ g(0) = -3(0) - 4 = 0 - 4 = -4 \]

  3. For \( x = 1 \): \[ g(1) = -3(1) - 4 = -3 - 4 = -7 \]

  4. For \( x = 3 \): \[ g(3) = -3(3) - 4 = -9 - 4 = -13 \]

  5. For \( x = 4 \): \[ g(4) = -3(4) - 4 = -12 - 4 = -16 \]

Now, we can fill in the function table:

\[ \begin{array}{|c|c|} \hline x & g(x) \ \hline -2 & 2 \ 0 & -4 \ 1 & -7 \ 3 & -13 \ 4 & -16 \ \hline \end{array} \]

what are the answers?

Here are the values of \( g(x) \) corresponding to each given \( x \):

\[ \begin{array}{|c|c|} \hline x & g(x) \ \hline -2 & 2 \ 0 & -4 \ 1 & -7 \ 3 & -13 \ 4 & -16 \ \hline \end{array} \]

So, the answers for each \( g(x) \) are:

  • \( g(-2) = 2 \)
  • \( g(0) = -4 \)
  • \( g(1) = -7 \)
  • \( g(3) = -13 \)
  • \( g(4) = -16 \)
A small publishing company is planning to publish a new book. Let C be the total cost of publishing the book (in dollars). Let N be the number of copies of the book produced. For the first printing, the company can produce up to 100 copies of the book. Suppose that C = 25N + 500 gives C as a function of N during the first printing.
Identify the correct description of the values in both the domain and range of the function. Then, for each, choose the most appropriate set of values.

Description of Values Set of Values
Domain:
number of copies produced
cost of publishing book (in dollars)
Domain: Set of Values
Range:
number of copies produced
cost of publishing book (in dollars)
Range: Set of Values

responses
the set of all real numbers greater than 25
the set of all real numbers greater than 100
the set of all real numbers from 0 to 500
{500, 525, 550, 575, ..., 3000}
{0, 1, 2, 3, ..., 100}
{25, 50, 75, 100, ..., 500}

In the function \( C = 25N + 500 \), the variables represent the following:

  • \( N \) (the number of copies produced) can take values from 0 to 100, since the company can produce up to 100 copies.
  • \( C \) (the total cost) will depend on the values of \( N \).

Domain

  • The domain represents the allowable values of \( N \), which are the number of copies produced.
  • Since \( N \) can vary from 0 to 100, the domain is the set of integers from 0 to 100.

Domain Description: Number of copies produced
Domain Set of Values: {0, 1, 2, 3, ..., 100}

Range

  • To find the range, we substitute the minimum and maximum values of \( N \) into the cost function \( C \):
    • When \( N = 0 \): \[ C = 25(0) + 500 = 500 \]
    • When \( N = 100 \): \[ C = 25(100) + 500 = 2500 + 500 = 3000 \]
  • Therefore, as \( N \) varies from 0 to 100, \( C \) will vary from \( 500 \) to \( 3000 \).

Range Description: Cost of publishing book (in dollars)
Range Set of Values: {500, 525, 550, 575, ..., 3000}

Summary

So, the correct identifications are:

Domain:

  • Description: Number of copies produced
  • Set of Values: {0, 1, 2, 3, ..., 100}

Range:

  • Description: Cost of publishing book (in dollars)
  • Set of Values: {500, 525, 550, 575, ..., 3000}
Solve for V.
-5 = v/3 - 8
Simplify your answer as much as possible.

To solve for \( V \) in the equation

\[ -5 = \frac{V}{3} - 8, \]

follow these steps:

  1. Add 8 to both sides:

    \[ -5 + 8 = \frac{V}{3} \]

    This simplifies to:

    \[ 3 = \frac{V}{3}. \]

  2. Multiply both sides by 3 to eliminate the fraction:

    \[ 3 \times 3 = V \]

    Thus,

    \[ V = 9. \]

Therefore, the solution is:

\[ V = 9. \]

how to solve -6(w + 5) = 24

To solve the equation

\[ -6(w + 5) = 24, \]

follow these steps:

  1. Distribute \(-6\) on the left side:

    \[ -6w - 30 = 24. \]

  2. Add \(30\) to both sides to isolate the term with \(w\):

    \[ -6w - 30 + 30 = 24 + 30, \]

    simplifying to:

    \[ -6w = 54. \]

  3. Divide both sides by \(-6\) to solve for \(w\):

    \[ w = \frac{54}{-6}. \]

    Simplifying this gives:

    \[ w = -9. \]

Thus, the solution is

\[ w = -9. \]

The equation -6(w + 5) = 24 is solved in several steps below.
For each step, choose the reason that best justifies it.
-6(w + 5)/-6 = 24/-6
w + 5 = -4
w + 5 - 5 = -4 - 5
w = -9

responses
addition property of equality
subtraction property of equality
multiplication property of equality
division property of equality
simplifying
Distributive Property

Let's analyze each step and identify the appropriate justification:

  1. Step: \(-6(w + 5)/-6 = 24/-6\)
    Reason: Division property of equality
    (We divide both sides by \(-6\).)

  2. Step: \(w + 5 = -4\)
    Reason: Simplifying
    (This is the result of simplifying the left side.)

  3. Step: \(w + 5 - 5 = -4 - 5\)
    Reason: Subtraction property of equality
    (We subtract \(5\) from both sides.)

  4. Step: \(w = -9\)
    Reason: Simplifying
    (This is the final simplification of the right side.)

So, the justifications are as follows:

  1. Division property of equality
  2. Simplifying
  3. Subtraction property of equality
  4. Simplifying