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You notice a hot air balloon descending. The elevation h
(in feet) of the balloon is modeled by the function h(x)=−8x+360,
where x
is the time (in seconds) since you first noticed the hot air balloon.

Graph the function and specify its domain and range. Then interpret the slope and intercepts of the graph.

Respuesta :

Answer:

the domain is 0 x 45 and the range is 0 h 360. The slope is -8, so the change in the height of the ballon is -8 feet per second. The h-intercept is 360, so the height of the ballon when the first noticed it was 360 feet. The x-intercept is 45, so the time it took the hot air balloon to reach the ground was 45 seconds.

Step-by-step explanation:

MrRoyal

The descending balloon is an illustration of a linear function.

  • The balloon spent 45 seconds in air  
  • The balloon was at a height of 360 feet when you noticed it.
  • The balloon descends 8 feet per seconds.
  • [tex]\mathbf{Domain=[0,45]}[/tex].
  • [tex]\mathbf{Range=[0,360]}[/tex]

The function is given as:

[tex]\mathbf{h(x) = -8x + 360}[/tex]

See attachment for the graph of h(x)

From the graph, we have the following observations

  • The y value ranges from 0 to 360
  • The x value ranges from 0 to 45
  • The function crosses the graph at x = 45 and y = 350

The above highlights mean that:

  • [tex]\mathbf{Domain=[0,45]}[/tex]
  • [tex]\mathbf{Range=[0,360]}[/tex]
  • [tex]\mathbf{x-intercept = 45}[/tex]
  • [tex]\mathbf{y-intercept = 360}[/tex]

The x intercept means that:

The balloon spent 45 seconds in air  

The y-intercept means that:

The balloon was at a height of 360 feet when you noticed it.

A linear function is represented as:

[tex]\mathbf{y = mx + c}[/tex]

Where:

m represents the slope

By comparison with [tex]\mathbf{h(x) = -8x + 360}[/tex]

[tex]\mathbf{m = -8}[/tex]

The above value of slope means that:

The balloon descends 8 feet per seconds

Read more about linear functions at:

https://brainly.com/question/20286983

Ver imagen MrRoyal

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