Respuesta :
The ordered pairs, justification of the function with different order pairs is required.
The ordered pairs are [tex](0,10),(1,9.5),(2,9),(3,8.5),(4,8),(5,7.5)[/tex]
All values of [tex]x[/tex] has a unique value in [tex]y[/tex] so, it is a function.
y = Height of candle
x = Number of hours
m = Rate = 0.5 inches per hour
c = y intercept = Initial height = 10 inches
The required function is
[tex]y=-0.5x+10[/tex]
Six ordered pairs would be
[tex]x=0,1,2,3,4,5[/tex]
[tex]y=-0.5\times 0+10=10[/tex]
[tex]y=-0.5\times 1+10=9.5[/tex]
[tex]y=-0.5\times 2+10=9[/tex]
[tex]y=-0.5\times 3+10=8.5[/tex]
[tex]y=-0.5\times 4+10=8[/tex]
[tex]y=-0.5\times 5+10=7.5[/tex]
The ordered pairs are
[tex](0,10),(1,9.5),(2,9),(3,8.5),(4,8),(5,7.5)[/tex]
It can be seen that all values of [tex]x[/tex] has a unique value in [tex]y[/tex] so, it is a function.
If m = 0.75 inches per hour
The function would change to
[tex]y=-0.75x+10[/tex]
Some ordered pairs would be
[tex]y=-0.75\times 0+10[/tex]
[tex]y=-0.75\times 1+10[/tex]
[tex](0,10),(1,9.25)[/tex]
The same is seen in this function, all values of [tex]x[/tex] has a unique value in [tex]y[/tex] so, it is a function.
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