anonymous
  • anonymous
does anyone know how to determine interval using < and > signs
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
you mean solve inequalities?
anonymous
  • anonymous
or interval notation?
anonymous
  • anonymous
i got a question to find the missing numbers and plot the graph and determine the intervals for which f(x)\[\ge\]0

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anonymous
  • anonymous
ok, what are the numbers?
anonymous
  • anonymous
and what is f(x)
anonymous
  • anonymous
first you have to find when f(x)=0, this divides the domain up into intervals. you then test a sample from each interval to see if its positive, negative, or zero
anonymous
  • anonymous
also find when f(x) is undefined
anonymous
  • anonymous
yes i did that but it is suppose to look like this: -3x^2+4x+4<0 x<-0.666 or x>2
anonymous
  • anonymous
x -3,-2,-1.5,-1,0,1,2 f(x) -7,0,2,3,2,-3,-12
anonymous
  • anonymous
3x^2-4x-4>0 3x^2-4x-4=0 3x^2-6x+2x-4=0 3x(x-2)+2(x-2)=0 (x-2)(3x+2)=0 x=2, -2/3 this divides the domain up into three intervals (-infinity, -2/3), (-2/3, 2), (2, infinity)
anonymous
  • anonymous
After plotting the graph for that it asks 3 questions: i. The coordinates of the maximum point ii. The interval for which􀀁f(x) ≥ 0 iii. The interval for which f(x) ≤ 0
anonymous
  • anonymous
so here you test a value from each interval. for the first interval we'll test x=-1 (x-2)(3x+2)>0 (negative)(negative)>0, true, this interval is part of the solution 2nd interval, we'll use 0 (negative)(positive)>0 false, this is not part of solution 3rd interval, we'll use x=3 (positive)(positive)>0, true, this is part of solution solution set: (-infinity, -2/3)U(2, infinity)
anonymous
  • anonymous
Im doing college algebra
anonymous
  • anonymous
so your question was which one?
anonymous
  • anonymous
did you plot the graph?
anonymous
  • anonymous
the last 2, yes I did the graph already
anonymous
  • anonymous
what was the shape of graph? parabola?
anonymous
  • anonymous
it is mountain shaped
anonymous
  • anonymous
let me plot it, 1 second
anonymous
  • anonymous
f(x)=2-3x-2x^2
anonymous
  • anonymous
yes i just did a regression and got -2x^2-3x+2, it is a parabola
anonymous
  • anonymous
ok
anonymous
  • anonymous
website crashed on me
anonymous
  • anonymous
the maximum can be solved by finding the y-coordinate of the vertex, it's a maximum because the parabola opens down
anonymous
  • anonymous
for that i got -1,3
anonymous
  • anonymous
you got -1, 3 for what?
anonymous
  • anonymous
the maximum point
anonymous
  • anonymous
not quite, from the regression we have f(x)=-2x^2-3x+2
anonymous
  • anonymous
the vertex is at (3/[2(-2)], f(3/[2(-2)]) or (-3/4, 25/8)
anonymous
  • anonymous
so the max value is 25/8
anonymous
  • anonymous
ok I think you are more advance for what the instructor wants he said to look at the graph and just write down the coordinates of the max point
anonymous
  • anonymous
ah ok, but does he want you to solve the inequalities or just look at the graph?
anonymous
  • anonymous
yes I solved it but he want it in a format that I'm not so clear on
anonymous
  • anonymous
interval notation?
anonymous
  • anonymous
or set-builder notation?
anonymous
  • anonymous
I solved it ad got: 0.5 and -2
anonymous
  • anonymous
ok, so now you have the intervals you need to solve the inequality
anonymous
  • anonymous
in and example he has x^2-3x+2>0 answer: x<1 or x>2
anonymous
  • anonymous
this splits the domain into 3 intervals
anonymous
  • anonymous
ok so you have the zeros of f(x) in your question, 1/2 and -2
anonymous
  • anonymous
so the factored form of f(x) is (2x-1)(x+2)
anonymous
  • anonymous
but I solved the inequality 2-3x-2x^2|dw:1332811990724:dw| and got 0.5 and -2
anonymous
  • anonymous
you didn't solve the inequality, you solved the equation 2-3x-2x^2=0
anonymous
  • anonymous
it was not equal to 0 it was greater than or equal to 0
anonymous
  • anonymous
yeah, that's the next step, solving the inequality, which is easy when you found the zeros
anonymous
  • anonymous
|dw:1332812190676:dw|
anonymous
  • anonymous
these 2 zeros split the domain into 3 intervals, every number from each interval will be either positive or negative (less than 0 or greater than 0)
anonymous
  • anonymous
this is what i have |dw:1332812252593:dw|
anonymous
  • anonymous
so from this, the x-axis is y=0. which intervals is f(x) >=0?
anonymous
  • anonymous
f(x)>0 for the parts of the graph that are above the x-axis
anonymous
  • anonymous
Im just not sure how it should be written x\[\le-2 or x \ge0.5\]
anonymous
  • anonymous
you don't use the word OR here, you use AND because this is a conjunction, not a disjunction. you would write \[x \ge -2 and x \le \frac{1}{2}\] This is better written like this though: \[-2 \le x \le \frac{1}{2}\]
anonymous
  • anonymous
ok
anonymous
  • anonymous
you would use the word or for the <= solutions though, because that is a disjunction
anonymous
  • anonymous
can you please explain when to use the signs
anonymous
  • anonymous
ok
anonymous
  • anonymous
which signs? \[\le\] and \[\ge\]?
anonymous
  • anonymous
when the solution is a range of values like between -2 and 1/2, you use inequality signs. if the solutions are ONLY 1/2 and -2, you use the = sign
anonymous
  • anonymous
-2<=x<=1/2 means that every x between those 2 numbers is a solution
anonymous
  • anonymous
yes like the 3rd question asks the same thing but turns the sign the other way
anonymous
  • anonymous
\[\le\] means less than or equal to \[\ge\] means greater than or equal to
anonymous
  • anonymous
i had it the wrong way
anonymous
  • anonymous
do you understand?
anonymous
  • anonymous
I just not getting it look at the ques
anonymous
  • anonymous
the interval for which f(x) is less than or eqaul to 0 is all x-values where the graph is at the x-axis or below it
anonymous
  • anonymous
if i have the exact same eqution but he signs are turned opposite direction how do I know which sign to use wouldn't the same number always be less or greater
anonymous
  • anonymous
if x<1, x can be 0 if x>1, x cannot be 0
anonymous
  • anonymous
the sign you use depends on the solution. just because you have a < sign in the question doesn't mean that you use a < in the answer. the answer can have a > sign
anonymous
  • anonymous
yes but remember that he uses the format where i use both signs in the ans
anonymous
  • anonymous
thats because you have to do that with a disjunction (when you use the word or), but with a conjunction, you don't have to
anonymous
  • anonymous
oh
anonymous
  • anonymous
-2-2 and x<1/2
anonymous
  • anonymous
yea
anonymous
  • anonymous
so then the ans for 2-3x-2x^2\[leo would be x \le-2&x \ge0.5\]
anonymous
  • anonymous
the answer for 2-3x-2x^2<=0 is x<=-2 OR x>=0.5
anonymous
  • anonymous
because x can't be less than -2 and greater than 0.5 at the same time, right?
anonymous
  • anonymous
ok i get it now
anonymous
  • anonymous
thank you very much for your help
anonymous
  • anonymous
glad i could help
anonymous
  • anonymous
it says on the same graph I should Draw the line g􀀎(x) = x − 1 on the same graph

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