SOLUTION: 1) Determine the average rate of change for the function: f(x)= x^2 + 10x +16 where -3 is less than or equal to x is less than or equal to 3 2) Find the domain of the giv

Algebra ->  Algebra  -> Rational-functions -> SOLUTION: 1) Determine the average rate of change for the function: f(x)= x^2 + 10x +16 where -3 is less than or equal to x is less than or equal to 3 2) Find the domain of the giv      Log On

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Question 98271: 1)
Determine the average rate of change for the function:
f(x)= x^2 + 10x +16 where -3 is less than or equal to x is less than or equal to 3

2) Find the domain of the given function
http://www.webassign.net/www21/symImages/9/6/91b1c4f55e28b2d77681409dffacec.gif
3) Write the domain of the rational function in interval notation as
http://www.webassign.net/www21/symImages/3/e/35f8505dfa1bc3d278590bcb5943d2.gif
(P.S - If you haven't figured it out yet, I'm the person who has been posting all the questions about functions for the past week. Thank you all so much for your help! I really appreciate it)

Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
1)
To find average rate between two points on a graph, simply draw a line through those two points and find the slope

So the x values of the points are given as x=-3 and x=3

Now we need to find the y values at the given x-values:

Plug in x=-3 to find the value of y at x=-3

f%28-3%29=+%28-3%29%5E2+%2B+10%28-3%29+%2B16 Plug in x=-3


f%28-3%29=+-5 Evaluate



Now plug in x=3 to find the value of y at x=3

f%28-3%29=+%283%29%5E2+%2B+10%283%29+%2B16 Plug in x=3


f%28-3%29=+55 Evaluate

Now that we have the two points (-3,-5) and (3,55) we can find the slope through these points

m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Now start with the slope formula


m=%2855--5%29%2F%283--3%29 plug in x%5B1%5D=-3, x%5B2%5D=3, y%5B1%5D=-5 and y%5B2%5D=55


m=%2860%29%2F%286%29 Subtract


m=10 Divide


So the average rate of change is 10


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2)
K%28v%29=%282v%5E2-9%29%2F%28v%5E2-v-30%29Start with the given function


v%5E2-v-30=0 Set the denominator equal to zero




%28v-6%29%28v%2B5%29=0 Factor the left side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:

v-6=0 or v%2B5=0

v=6 or v=-5 Now solve for v in each case




Since v=6 or v=-5 make the denominator equal to zero, that means we must exclude these values from the domain.

So our domain is: v is the set of all real numbers except v%3C%3E6 or v%3C%3E-5

Which looks like this in interval notation:


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3)
f%28x%29=%281%29%2F%28x-20%29Start with the given function


x-20=0 Set the denominator equal to zero


x=20 Add 20 to both sides


Since x=20 makes the denominator equal to zero, that means we must exclude this value from the domain.

So our domain is: x is the set of all real numbers except v%3C%3E20

Which looks like this in interval notation: