You are here:

Advanced Math/graphing functions

Advertisement

Expert: - 9/3/2009


Question
QUESTION: sketch the graph of each function
a) f(x)= absolute value of(x+3) -2
b) g(x)= 1/f(x)

ANSWER: (a) The line would be at a perfect 45 degree angle with an upwards slope in both directions.
|x+3| is 0 when x = -3, so |x+3| - 2 is -2 at x = -3.

This means that it forms a line sloping up from the point (-3,-2)
in both directions at a 45 degree angle.

(b) When f(x) is 1, the functions have the same value.  

When f(x) is 0, g(x) is undefined, so it has an inflection point at these values.

Note that f(x) = 0 is at x+3 = 2 and -x-3 = 2.  That is, x = -1 or x = -5.

Since f(x) is always positive, g(x) is also always positive.

So at the two inflection points, g(x) goes off to +infinity.

As x goes of to +/- infinity, g(x) goes to 0.


---------- FOLLOW-UP ----------

QUESTION: how would i go about graphing (b)?

Answer
Graph
Graph  
a) f(x)= absolute value of(x+3) -2
b) g(x)= 1/f(x)

To graph f(x), note that it is two lines with slope -1 and 1.
They meet at x = -3.  At that point, the function f(x) has a value of -2.
The lines would cross the x axis at -1 and -5.

To graph the function g(x), note that g(x) = 1/f(x).
That means where f(x) is 0, the function is undefined.  That happens where x=-1 and x =-5.
Where f(x) goes off to infinity, g(x) goes to 0.
This happens as x goes off to infinity and minus infinity.



When x>-1 and x<-5, f(x) is positive, which means g(x) is positive.

As the line x=-1 is approached from the left, g(x) goes off to infinity.
As the line x=5 is approached from the right, g(x) goes off to infiniy.

t x = 2 and x = 4, the value of g(x) = 1.

When -5<x<-1, f(x) is negative, so g(x) is negative.
When x=-4 or x=-2, the value of f(x) is -1, so the value of g(x) is -1.
The value of f(-3) is -2, so the value of g(-3) is -1/2.
The function g(x) goes to -infinity as it nears -5 from the right.
The function g(x) goes to -infinity as it nears -1 from the left.

Apply these two the picture sent.  

Advanced Math

All Answers

Answers by Expert:

Ask Experts

Volunteer

Scott A Wilson

Expertise

I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can even tell you it takes me over 2,000 steps to go a mile, but is that relevant?

Experience

Experience in the area; I have tutored people in the above areas of mathematics for almost two years in AllExperts.com. I have tutored people here and there in mathematics since before I received a BS degree almost 25 years ago. In just two more years, I received an MS degree as well, but more on that later. I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman. I tutored at Mathnasium for well over a year. I worked at The Boeing Company for over 5 years. I received an MS degreee in Mathematics from Oregon State Univeristy. The classes I took were over 100 hours of upper division credits in mathematical courses such as calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more. I graduated with honors in both my BS and MS degrees. Past/Present Clients: College Students at Oregon State University, various math people since college, over 7,500 people on the PC from the US and rest the world.

Publications
My master's paper was published in the OSU journal. The subject of it was Numerical Analysis used in shock waves and rarefaction fans. It dealt with discontinuities that arose over time. They were solved using the Leap Frog method. That method was used and improvements of it were shown. The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.

Education/Credentials
Master of Science at OSU with high honors in mathematics. Bachelor of Science at OSU with high honors in mathematical sciences. This degree involved mathematics, statistics, and computer science. I also took sophmore level physics and chemistry while I was attending college. On the side I took raquetball, but that's still not relevant.

Awards and Honors
I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes in mathematics, I was first. In a class of over 100 students, I was always one of the first ones to complete the test. I graduated with well over 50 credits in upper division mathematics.

Past/Present Clients
My clients have been students at OSU, people nearby, friends with math questions, and several people every day on the PC, and you're probably make one more.

©2012 About.com, a part of The New York Times Company. All rights reserved.