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For the function g, g(3)= -11 and g(7)= 5. What is the function rule for g(x)?

User Dfang
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1 Answer

8 votes
8 votes

Answer:

g(x) = 4x - 23

Explanation:

We will assume a linear function for g(x)

This will be of the form g(x) = ax + b where a and b are constants

Given the info,

g(3) = a(3) + b = -11

g(7) = a(7) + b = 5

Thus we have two equations in a and b
3a + b = -11 [1]
7a + b = 5 [2]

Subtract [1] from [2]:
7a + b - (3a + b) = 5 - (-11)
7a + b - 3a - b = 5 + 11

4a = 16

a = 4

Substitute for a in equation [2]:

4(7) + b = 5
28 + b = 5

b = 5-28 = -23

So equation of g(x) is
g(x) = 4x - 23

User Joesph
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