The given data are linear functions having a standard form of A·x + B·y = C
The required values are;
- f(-3) = -21
- f(-3) = 14
- f(-3) = -5
- Please find attached the graph of the function f(x) = 3·x - 6
- Please find attached the graph of the function f(x) = -2·(x + 4)
- Please find attached the graph of the function [tex]f(x) = \dfrac{1}{2} \cdot x + 5[/tex]
- The function that represents the data is f(x) = 0.2·x
- The function representing the data is f(x) = 3·x + 5
- The function that corresponds with the data is f(x) = 3·x + 5
- The range of the function is 5 ≤ f(x) ≤ 205
- The linear function is t = 60 + 125·tThe total cos for two years of service is $3,060
Reasons:
Value of f(-3) for the given functions
1. f(x) = 4·x - 9
f(-3) = 4 × (-3) - 9 = -21
2. [tex]f(x) = -\dfrac{1}{3} \cdot x + 13[/tex]
[tex]f(-3) = -\dfrac{1}{3} \times (-3) + 13 = 14[/tex]
3. f(x) = -2·x - 11
f(-3) = -2 × (-3) - 11 = -5
4. Please find the graph of f(x) = 3·x - 6, created with MS Excel
5. Please find attached the graph of f(x) = -2·(x + 4)
6. Please find attached the graph [tex]f(x) = \dfrac{1}{2} \cdot x + 5[/tex]
7. The slope, m, of the function in the table is given as follows;
[tex]Slope, \, m =\dfrac{0.2-(-0.6)}{1-(-3)} = \dfrac{1.4-0.2}{1-7} = 0.2[/tex]
The equation of the data is therefore;
y - 1.4 = 0.2·(x - 7)
y = 0.2·x - 1.4 + 1.4 = 0.2·x
Therefore, we have;
8. The slope, m, of the data is given as follows;
[tex]Slope, \, m =\dfrac{17-(-1)}{4-(-2)} = \dfrac{-1-(-10)}{-2-(-5)} = 3[/tex]
The equation of the data is therefore;
y - 17 = 3·(x - 4)
y - 17 = 3·x - 12
y = 3·x - 12 + 17 = 3·x + 5
Therefore, we have;
9. The data in the table has the following slope, m;
[tex]Slope, \, m =\dfrac{-18-2}{8-(-2)} = \dfrac{2- 8}{-2-(-5)} = -2[/tex]
The equation of the data is therefore;
y - (-18) = -2·(x - 8)
y - (-18) = -2·x + 16
y = -2·x + 16 - 18 = -2·x - 2
Therefore, we have;
10. The given function is f(x) = 4·x + 5
The given domain of the function is 0 ≤ x ≤ 50
The range of the of the function is given as follows;
Which gives;
4 × 0 + 5 ≤ f(x) ≤ 4 × 50 + 5
The range of the function is therefore;
11. The activation fee charged by the television provider = $60
The cost per month = $125
- The linear function that represent the total cost, is t = 60 + 125·t
Part 2
Number of months in two years, t = 2 years × 12 months/year = 24 months
Total cost for two years, is t₂₄ = 60 + 125 × 24 = 3,060
- Total cost for two years, t₂₄ is $3,060
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