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!