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ruslelena [56]
3 years ago
13

Identify the range of the function. A) (2, 8) B) [2, 8] C) (−5, 9) D) [−5, 9]

Mathematics
1 answer:
Ivanshal [37]3 years ago
5 0

Answer:

The answer is "Option A"

Step-by-step explanation:

The domain is the collection of the value, which belongs to the separate variable (horizontal axis). So, to find a region with a graph, it must search for the function, which starts and end. And at all these levels we are searching at x-values.  

Its starting point is (2,9) and the ending point is (8,3).  Therefore, x= 2 to x=8 is the domain.

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Step-by-step explanation:

To find the solution of the graph let us make the equation of the line by using any two points on the line

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  • b is the y-intercept (value y at x = 0)

The formula of the slope is m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}

From the figure

∵ The line passes through points (-3 , 0) and (0 , 1)

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- Substitute the value of m in the form of the equation

∴ y = \frac{1}{3} x + b

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∴ b = 1

∴ y = \frac{1}{3} x + 1

Lets substitute the x-coordinate of each point to find the y-coordinate, if the y-coordinate is equal to the y-coordinate of the points, then the point is a solution

Point (-15 , -4)

∵ x = -15

∴ y = \frac{1}{3} (-15) + 1

∴ y = -5 + 1 = -4 ⇒ same value of the point

∴ (-15 , -4) is a solution

Point (-6 , 1)

∵ x = -6

∴ y = \frac{1}{3} (-6) + 1

∴ y = -2 + 1 = -1 ⇒ not the same value of the point

∴ (-6 , 1) is not a solution

Point (3 , 2)

∵ x = 3

∴ y = \frac{1}{3} (3) + 1

∴ y = 1 + 1 = 2 ⇒ same value of the point

∴ (3 , 2) is a solution

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∵ x = 12

∴ y = \frac{1}{3} (12) + 1

∴ y = 4 + 1 = 5 ⇒ not the same value of the point

∴ (12 , 9) is not a solution

Point (21 , 8)

∵ x = 21

∴ y = \frac{1}{3} (21) + 1

∴ y = 7 + 1 = 8 ⇒ same value of the point

∴ (21 , 8) is a solution

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3 years ago
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