Respuesta :

Ashraf82

Answer:

The point (4.5 , 6) lies on the graph

Step-by-step explanation:

* Lets explain how to prove that a point lies on a graph

- Substitute x and y by the coordinates of the point, if the

 left hand side (L.H.S) equals the right hand side (R.H.S) then the

 point lies on the graph OR

- Substitute x by the x-coordinate of the point to find y if the the

 value of y equals the y-coordinate of the point, then the point lies

 on the graph OR

- Substitute y by the y-coordinate of the point to find x if the the

 value of x equals the x-coordinate of the point, then the point lies

 on the graph

* Lets solve the problem

∵ The equation is y = 1.5 + 5

# Point (-4.5 , -2.5)

∵ x = -4.5 and y = -2.5

∴ -2.5 = 1.5 + (-4.5)

- Remember (+)(-) = (-)

∴ -2.5 = 1.5 - 4.5

∴ -2.5 = -3

∵ L.H.S ≠ R.H.S

∴ The point (-4.5 , -2.5) does not lie on the graph

# Point (-0.8 , 0.5)

∵ x = -0.8 and y = 0.5

∴ 0.5 = 1.5 + (-0.8)

∴ 0.5 = 1.5 - 0.8

∴ 0.5 = 0.7

∵ L.H.S ≠ R.H.S

∴ The point (-0.8 , 0.5) does not lie on the graph

# Point (7.9 , 9.5)

∵ x = 7.9 and y = 9.5

∴ 9.5 = 1.5 + 7.9

∴ 9.5 = 9.4

∵ L.H.S ≠ R.H.S

∴ The point (7.9 , 9.5) does not lie on the graph

# Point (4.5 , 6)

∵ x = 4.5 and y = 6

∴ 6 = 1.5 + 4.5

∴ 6 = 6

∵ L.H.S = R.H.S

∴ The point (4.5 , 6) lies on the graph

OR

∵ x = 4.5

∴ y = 1.5 + 4.5

∴ y = 6 ⇒ same value of the y-coordinate of the point

∴ The point (4.5 , 6) lies on the graph

OR

∵ y = 6

∴ 6 = 1.5 + x

- Subtract 1.5 from both sides

∴ 4.5 = x ⇒ same value of the x-coordinate of the point

∴ The point (4.5 , 6) lies on the graph

# Point (1.3 , 3.5)

∵ x = 1.3 and y = 3.5

∴ 3.5 = 1.5 + 1.3

∴ 3.5 = 2.8

∵ L.H.S ≠ R.H.S

∴ The point (1.3 , 3.5) does not lie on the graph

xero099

The points [tex](-0.8, 0.5)[/tex], [tex](7.9, 9.5)[/tex] and [tex](1.3, 3.5)[/tex] belong to the function [tex]y = 1.5 + \lceil x \rceil[/tex].

How to evaluate an absolute value function

In this question we must evaluate a function at given [tex]x[/tex]-values and determine if each point belong to the given expression:

[tex]y = 1.5 + \lceil x \rceil[/tex]    (1)

The x-component represents a ceiling function. Now we proceed to evaluate the function:

x = -4.5

[tex]y = 1.5 + \lceil -4.5 \rceil[/tex]

[tex]y = 1.5-5[/tex]

[tex]y = -3.5[/tex]

x = -0.8

[tex]y =1.5+\lceil -0.8\rceil[/tex]

[tex]y = 1.5 - 1[/tex]

[tex]y = 0.5[/tex]

x = 7.9

[tex]y = 1.5+\lceil 7.9\rceil[/tex]

[tex]y = 1.5+8[/tex]

[tex]y = 9.5[/tex]

x = 4.5

[tex]y = 1.5 + \lceil 4.5\rceil[/tex]

[tex]y = 1.5+5[/tex]

[tex]y = 6.5[/tex]

x = 1.3

[tex]y = 1.5 + \lceil 1.3 \rceil[/tex]

[tex]y = 1.5 + 2[/tex]

[tex]y = 3.5[/tex]

The points [tex](-0.8, 0.5)[/tex], [tex](7.9, 9.5)[/tex] and [tex](1.3, 3.5)[/tex] belong to the function [tex]y = 1.5 + \lceil x \rceil[/tex]. [tex]\blacksquare[/tex]

To learn more on functions, we kindly invite to check this verified question: https://brainly.com/question/5245372

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