Identify intervals on which the function is increasing, decreasing, or constant. g(x) = 2 - (x - 7)2 Increasing: x 2 Increasing: x -7 Increasing: x 7 Increasing: x 2; decreasing: x

Question

Identify intervals on which the function is increasing, decreasing, or constant. g(x) = 2 - (x - 7)2 Increasing: x < 2; decreasing: x > 2 Increasing: x < -7; decreasing: x > -7 Increasing: x < 7; decreasing: x > 7 Increasing: x > 2; decreasing: x < 2

jdoe0001 · Answer

http://nayak2010.files.wordpress.com/2011/01/picture-of-vertex-form-of-parabola.png <--- vertex form of a parabola

jdoe0001 · Answer

keep in mind that $\bf g(x) = 2 - (x - 7)^2\implies g(x) = - (x - 7)^2+2$

at the vertex is where the parabola changes from decreasing to increasing or the viceversa

anonymous · Answer

ok so how do I start to solve this problem?

jdoe0001 · Answer

well... what do you think would be the vertex for it?

anonymous · Answer

i know that to find vertex of something you can graph it and look at the peak of the parbala and that's the vertex

anonymous · Answer

and this one is just a straight line so its endless

jdoe0001 · Answer

right... well is not a straight line, $\bf g(x) = 2 - (x - 7)^2$

jdoe0001 · Answer

unless you meant $\bf g(x) = 2 - (x - 7)2$

anonymous · Answer

yes sir that's what i grapghed your last oe you typed

anonymous · Answer

ok so the vertex is 2 correct

jdoe0001 · Answer

|dw:1380656271522:dw|

anonymous · Answer

oh so its how do i know which > < it is? i know its going to be 2 though just not sure which > < it is

jdoe0001 · Answer

a function is increasing when it greater as it moves towards the right-side
and decreases as it's lesser as it moves towards the right-side

anonymous · Answer

Increasing: x > 2; decreasing: x < 2 Increasing: x < 2; decreasing: x > 2 how do i tell which one of these it is they both say increasing and decreasing they just have different greater than or less than signs

jdoe0001 · Answer

2-(x-7)2   =>   16-x

anonymous · Answer

-_- im sorry what

jdoe0001 · Answer

so, let us graph that... .let's say use 2 points

y = 16-x

x = 0
y = 16-0   => y = 16          so ( 0, 16 )

x =10
y = 16-10   => y = 6           so ( 10, 6)

|dw:1380656809080:dw|

anonymous · Answer

so its this one  Increasing: x < 2; decreasing: x > 2

jdoe0001 · Answer

well... notice, if it's a straight line, it's just decreasing

jdoe0001 · Answer

but I'd think it's a parabola

anonymous · Answer

like those are my answers and all of them both have increasing and decreasing on them

jdoe0001 · Answer

yeap, meaning is $\bf g(x) = 2 - (x - 7)^2$

anonymous · Answer

so im right?