SOLUTION: Draw the graphs of the following functions. The x- and y-intercepts of each graph should be labeled with their values, any vertex should be labeled with its coordinates. Show each

Algebra ->  Functions -> SOLUTION: Draw the graphs of the following functions. The x- and y-intercepts of each graph should be labeled with their values, any vertex should be labeled with its coordinates. Show each       Log On


   

Question 907200: Draw the graphs of the following functions. The x- and y-intercepts of each graph should be labeled with their values, any vertex should be labeled with its coordinates. Show each vertical or horizontal asymptotes with a dotted line and label it with its intercept value.

a. y = abs%283x+-+9%29
b. y = +x%5E3+-+8+
c. y = +5++-%093%2Fx++

if you can't draw the graph please explain how I would find it or what it would look like.
Thanks!
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Although is was not complete, a sufficient response was already given:

http://www.algebra.com/algebra/homework/Functions/Functions.faq.question.906687.html

For part (b), that would simply be the standard model cubic function shifted downward by 8 units. Instead of the inflection point at (0,0), the inflection point moves to (0,-8).

Part (b) graph:
graph%28300%2C300%2C-10%2C10%2C-12%2C8%2Cx%5E3-8%29

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
a. +y+=++abs%283x+-+9%29+
The x-intercept is y=0; +0+=++abs%283x+-+9%29+ => +0+=++sqrt%28%283x+-+9%29%5E2%29+ => +0+=+%283x+-+9%29+ or +0+=+-%283x+-+9%29+
so, if +0+=+%283x+-+9%29+ => 3x=9 => x=3
or
if +0+=+-%283x+-+9%29+ => -3x%2B9=0 => -3x=-9 => x=-9%2F-3=> x=3 ...x-intercept is at (3,+0+)

and y-intercept: set x=0
+y+=++abs%283%2A0+-+9%29+ => +y+=+sqrt%28%28+-+9%29%5E2%29+ => y=+9+...y-intercept is at (+0+,+9+)


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2Cabs%283x+-+9%29%29+


b.
y+=+x%5E3+-+8+
x-intercept: set y=0
0=+x%5E3+-+8+ => 8=+x%5E3++ => root%283%2C8%29=+x++=> root%283%2C2%5E3%29=+x++=> x+=2+ ...x-intercept is at (2,+0+)

y-intercept: set x=0
y+=+0%5E3+-+8+ => y=-8...y-intercept is at (+0+,+-8+)

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2Cx%5E3+-+8%29+


c. y+=++5++-%093%2Fx++
x-intercept: set y=0
0+=++5++-3%2Fx++
3%2Fx+=++5++
3+=++5x++
3%2F5+=++x++....x-intercept is at (3%2F5,+0+)

y-intercept: set x=0
y+=++5++-3%2F0++
y+=++5++-infinity++ ...there is no y-intercept

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C5++-3%2Fx%2C5%29+

has horizontal asymptote through y=5
5-3%2Fx->5+ as x->%2B-+infinity
vertical asymptote

5-3%2Fx -> %28%2B-infinity%29 as x -> 0