Functions question help please (1 Viewer)

[purplemoon]

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.

Cheers!

 

[nightweaver066]

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

 

[deswa1]

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.

 

[Timske]

y = 2x - 4

 

[purplemoon]

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]

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 =)

 

[purplemoon]

Why would you feel that way? It's part of the learning process =)

Yeah, you're actually right about that, thanks