Question

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

Answer 1

you mean solve inequalities?

Answer 2

or interval notation?

Answer 3

i got a question to find the missing numbers and plot the graph and determine the intervals for which f(x)\[\ge\]0

Answer 4

ok, what are the numbers?

Answer 5

and what is f(x)

Answer 6

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

Answer 7

also find when f(x) is undefined

Answer 8

yes i did that but it is suppose to look like this:
-3x^2+4x+4<0
x<-0.666 or x>2

Answer 9

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

Answer 10

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)

Answer 11

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

Answer 12

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)

Answer 13

Im doing college algebra

Answer 14

so your question was which one?

Answer 15

did you plot the graph?

Answer 16

the last 2, yes I did the graph already

Answer 17

what was the shape of graph? parabola?

Answer 18

it is mountain shaped

Answer 19

let me plot it, 1 second

Answer 20

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

Answer 21

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

Answer 22

ok

Answer 23

website crashed on me

Answer 24

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

Answer 25

for that i got -1,3

Answer 26

you got -1, 3 for what?

Answer 27

the maximum point

Answer 28

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

Answer 29

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

Answer 30

so the max value is 25/8

Answer 31

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

Answer 32

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

Answer 33

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

Answer 34

interval notation?

Answer 35

or set-builder notation?

Answer 36

I solved it ad got:
0.5 and -2

Answer 37

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

Answer 38

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

Answer 39

this splits the domain into 3 intervals

Answer 40

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

Answer 41

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

Answer 42

but I solved the inequality 2-3x-2x^2
and got 0.5 and -2

Answer 43

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

Answer 44

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

Answer 45

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