What is the domain and range of y=-0.7x+1.9 and y=0.7x+1.9?

AI Thread Summary
The discussion focuses on determining the domain and range of two linear functions representing the halves of a triangular roof: y = -0.7x + 1.9 for the left half and y = 0.7x + 1.9 for the right half. The left half has a domain of -2.7 to 0 and a range from 0 to 1.9, while the right half has a domain from 0 to 2.7 and the same range of 0 to 1.9. Participants emphasize the importance of graphing the functions to visualize the triangle's shape and confirm the maximum and minimum values of the range. The intersection point of the two lines at y = 1.9 is identified as the peak of the triangle, with the base at y = 0. Understanding these concepts is crucial for accurately modeling the triangular structure.
milliex51
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Homework Statement


State the domain and range of the function that models each half of the roof (triangle)


Homework Equations


Y= -0.7x+1.9 (left half)
Y= 0.7x+1.9 (right half)

The Attempt at a Solution



Why is the answer:

Left half: domain: −2.7≤x≤0 range: 0≤y≤1.9
Right half: Domain: 0≤x≤2.7 range: 0≤y≤1.9

I don't understand.
 
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Haven't you tried graphing this on your calculator?
 
yes I did, and I don't get how for the domain -2.7 is less than or equal to x less than or equal to 0?
 
If it's modelling a triangle, then draw a picture.

You'll see that the maximum value of the range is 1.9 (the intersection of the two lines) and the minimum is 0 (because a side of a triangle can't be negative).

Then solve the equations for y=0 and y=1.9 to get the values of the Domains.
 

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