Find the domain in interval notation: f(x) = Squareroot 3x + 1/x - 7 ii. Find th

Question

Find the domain in interval notation: f(x) = Squareroot 3x + 1/x - 7 ii. Find the average rate of change of f(x) = 5 - 4x^2 between x = 3 and x = 3 + h III. The population of a planned seaside community is P(t) = 3000 + 200t + 1t^2, t is the number of years since 1985. Find P(10), P(20) and the average rate of change between t = 10 and t = 20 and interpret the values. IV. Find the domain in interval notation: f(x) = Squareroot x^2 - 4x - 12 V Graph: f(x) = {-x if x lessthanorequalto 0 9 - x^2 if 0 3}

Explanation / Answer

1) given f(x)=((3x+1))/(x-7)

f(x) is defined when 3x+10,and x-70

x-1/3,and x7

domain is [-1/3,7)U(7,)

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2)f(x)=5-4x2

f(3)=5-4*32

f(3)=-31

f(3+h)=5-4*(3+h)2

f(3+h)=5-4*(9+6h+h2)

f(3+h)=5-36-24h-4h2

f(3+h)=-31-24h-4h2

average rate of change =[f(3+h)-f(3)]/[(3+h)-3]

average rate of change =[-31-24h-4h2+31]/h

average rate of change =[-24h-4h2]/h

average rate of change =-24-4h

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