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

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(35256) (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 and

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

Plug in to find the value of y at

Plug in

Evaluate

Now plug in to find the value of y at

Plug in

Evaluate

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

Now start with the slope formula

plug in , , and

Subtract

Divide

So the average rate of change is 10

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2)
Start with the given function

Set the denominator equal to zero

Factor the left side (note: if you need help with factoring, check out this solver)

Now set each factor equal to zero:

or

or Now solve for v in each case

Since or 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 or

Which looks like this in interval notation:

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3)
Start with the given function

Set the denominator equal to zero

Add 20 to both sides

Since 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

Which looks like this in interval notation:

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