# SAT Math Problem (1)

## SAT Question # 1

The graph of the rational function f, where

has vertical asymptotes at x= ____

a) 0 only

b) 4 only

c) 5 only

d) 0 and 4 only

e) 0, 4, and 5

This is a simple problem if you know the definition of asymptote and how to factor or use the quadratic formula. Both of which I have shown in previous posts, but this is Steemit, so I can reexplain for you because I love you!!! Haha.

#### Step 1

An **asymptote** is a line that is never crossed by the function. We find vertical asymptotes where the bottom of the fraction is zero (because you are never allowed to divide by zero), so we need to know the answer to

What x values make this true?

#### Step 2 (1 - Factor)

We need two numbers that multiply to equal 16 that add up to -8. Since the number in front of x squared is 1 , that is all we have to do! We recognize that these numbers are -4 and -4 because (-4)(-4)=+16 and -4+(-4)=-8.

Since they are the same we only get 1 solution. What makes x-4=0…. Well +4 does, our only answer.

#### Step 2 (2 – Quadratic Formula)

#### A bonus way (Graphically)

Again, knowing what an asymptote is solves the problem immediately with a graph. The red line is our asymptote and the equation for that line is x=4. Plus you clearly see that it is the only one!

Hope you've enjoyed the math for today Steemians! Happy trails and learn much to teach the kids!

superbuckles (46)7 years agoI had to learn this in school. The quadratic formula annoyed me, because I always messed it up.😂

hansenator (57)7 years agoLearn it now Rubiks champ!

superbuckles (46)7 years ago😂😂😂WILL DO!!!

rycharde (63)7 years agoVery good. We definitely need more question like these. What we really need are more students! They surely will come... soon-ish!

hansenator (57)7 years agoYeah. Let just hope they bring intelligent things to Steemit. Lol

rycharde (63)7 years agoAh, yes, we could see an infestation of "Only if you're a genius" questions.

hansenator (57)7 years ago (edited)I can bring it down a bit them. Haha. Let it entertain you! I'll be posting on my old research later on, trying to make it understandable for everyone.

theguruasia (67)7 years ago@hansenator,

Kill me, that's better! When I get those questions with those graph that's what I always felt :D

Anyway nice question.. but I don't know how to solve :D

Cheers~