does anyone know how to determine interval using < and > signs

- anonymous

does anyone know how to determine interval using < and > signs

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- anonymous

you mean solve inequalities?

- anonymous

or interval notation?

- 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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## More answers

- anonymous

ok, what are the numbers?

- anonymous

and what is f(x)

- 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

also find when f(x) is undefined

- 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

x -3,-2,-1.5,-1,0,1,2
f(x) -7,0,2,3,2,-3,-12

- 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

After plotting the graph for that it asks 3 questions:
i. The coordinates of the maximum point
ii. The interval for whichf(x) ≥ 0
iii. The interval for which f(x) ≤ 0

- 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

Im doing college algebra

- anonymous

so your question was which one?

- anonymous

did you plot the graph?

- anonymous

the last 2, yes I did the graph already

- anonymous

what was the shape of graph? parabola?

- anonymous

it is mountain shaped

- anonymous

let me plot it, 1 second

- anonymous

f(x)=2-3x-2x^2

- anonymous

yes i just did a regression and got -2x^2-3x+2, it is a parabola

- anonymous

ok

- anonymous

website crashed on me

- anonymous

the maximum can be solved by finding the y-coordinate of the vertex, it's a maximum because the parabola opens down

- anonymous

for that i got -1,3

- anonymous

you got -1, 3 for what?

- anonymous

the maximum point

- anonymous

not quite, from the regression we have f(x)=-2x^2-3x+2

- anonymous

the vertex is at (3/[2(-2)], f(3/[2(-2)]) or (-3/4, 25/8)

- anonymous

so the max value is 25/8

- 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

ah ok, but does he want you to solve the inequalities or just look at the graph?

- anonymous

yes I solved it but he want it in a format that I'm not so clear on

- anonymous

interval notation?

- anonymous

or set-builder notation?

- anonymous

I solved it ad got:
0.5 and -2

- anonymous

ok, so now you have the intervals you need to solve the inequality

- anonymous

in and example he has
x^2-3x+2>0
answer: x<1 or x>2

- anonymous

this splits the domain into 3 intervals

- anonymous

ok so you have the zeros of f(x) in your question, 1/2 and -2

- anonymous

so the factored form of f(x) is (2x-1)(x+2)

- anonymous

but I solved the inequality 2-3x-2x^2|dw:1332811990724:dw|
and got 0.5 and -2

- anonymous

you didn't solve the inequality, you solved the equation
2-3x-2x^2=0

- anonymous

it was not equal to 0 it was greater than or equal to 0

- anonymous

yeah, that's the next step, solving the inequality, which is easy when you found the zeros

- anonymous

|dw:1332812190676:dw|

- 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

this is what i have
|dw:1332812252593:dw|

- anonymous

so from this, the x-axis is y=0. which intervals is f(x) >=0?

- anonymous

f(x)>0 for the parts of the graph that are above the x-axis

- anonymous

Im just not sure how it should be written
x\[\le-2 or x \ge0.5\]

- 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

ok

- anonymous

you would use the word or for the <= solutions though, because that is a disjunction

- anonymous

can you please explain when to use the signs

- anonymous

ok

- anonymous

which signs? \[\le\] and \[\ge\]?

- 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

-2<=x<=1/2 means that every x between those 2 numbers is a solution

- anonymous

yes like the 3rd question asks the same thing but turns the sign the other way

- anonymous

\[\le\] means less than or equal to
\[\ge\] means greater than or equal to

- anonymous

i had it the wrong way

- anonymous

do you understand?

- anonymous

I just not getting it look at the ques

- 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

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

if x<1, x can be 0
if x>1, x cannot be 0

- 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

yes but remember that he uses the format where i use both signs in the ans

- 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

oh

- anonymous

-2-2 and x<1/2

- anonymous

yea

- anonymous

so then the ans for 2-3x-2x^2\[leo would be x \le-2&x \ge0.5\]

- anonymous

the answer for 2-3x-2x^2<=0 is
x<=-2 OR x>=0.5

- anonymous

because x can't be less than -2 and greater than 0.5 at the same time, right?

- anonymous

ok i get it now

- anonymous

thank you very much for your help

- anonymous

glad i could help

- anonymous

it says on the same graph I should Draw the line g(x) = x − 1 on the same graph

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