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Functions question help please (1 Viewer)

purplemoon

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This question has been kind of killing my life for the past i dont know how many hours. Help is greatly appreciated !!

Consider the linear function g(x), defined for x>= 0.
Given that g(3)=2 and g(4)=4; write down the rule that defines the function and state the range.

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nightweaver066

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Linear function, so it is in the form of g(x) = mx + b

g(3) = 3m + b = 2 ... (1)
g(4) = 4m + b = 4 ... (2)

(2) - (1): m = 2

From (1), 6 + b = 2
b = -4

Therefore g(x) = 2x - 4

Range: g(x) >= -4
 
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deswa1

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Look at the value inside g(x) as x and the output as y. Therefore it is a linear (straight line) that passes through the points (3,2) and (4,4). The equation of this line is y=2x-4. Therefore g(x)=2x-4. As g(x) is defined only for x is greater than or equal to zero, y is at least -4. Therefore the range is y is greater than or equal to -4.
 

purplemoon

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Oh my god. It never occurred to me to use simultaneous equations. Feeling so embarrasingly stupid at the moment haha :)

Thankyou all so much!!
 

Carrotsticks

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Oh my god. It never occurred to me to use simultaneous equations. Feeling so embarrasingly stupid at the moment haha :)

Thankyou all so much!!
Why would you feel that way? It's part of the learning process =)
 

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