Determine a graph which have x-intercepts, Algebra

Assignment Help:

Remember that a graph will have a y-intercept at the point (0, f (0)) .  Though, in this case we have to ignore x = 0 and thus this graph will never cross the y-axis. It does get extremely close to the y-axis, but it will never cross or touch it & thus no y-intercept.

Next, remember that we can determine where a graph will have x-intercepts by solving f ( x ) = 0 .

For rational functions this might seem like a mess to deal along with.  Though, there is a nice fact regarding rational functions which we can use here.  A rational function will be zero at a specific value of x only if the numerator is zero at that x & the denominator isn't zero at that x.  In other terms, to determine if a rational function is ever zero all that we need to do is set the numerator equal to zero & solve.  Once we have these solutions we just need to check that none of them make the denominator zero as well.

In our case the numerator is one and will never be zero and so this function will have no x- intercepts.  Again, the graph will get extremely close to the x-axis but it will never touch or cross it.

At last, we have to address the fact that graph gets extremely close to the x and y-axis but never crosses.  Since there isn't anything special about the axis themselves we'll use the fact that the x- axis is actually the line specified by y =0 and the y-axis is really the line specified by x = 0.


Related Discussions:- Determine a graph which have x-intercepts

Properties of logarithms, Properties of Logarithms 1. log b 1 = 0 .  It...

Properties of Logarithms 1. log b 1 = 0 .  It follows from the fact that b o   = 1. 2. log b b = 1.  It follows from the fact that b 1 = b . 3. log b b x   = x .  it c

Truth table-boolean expressions, 1. Construct a truth table for the followi...

1. Construct a truth table for the following Boolean expressions: a) ABC + A'B'C' b) ABC + AB'C' + A'B'C' c) A (BC' + B'C) 2.   Simplify the following expressions:

Draw the graph parabolas, Sketch the graph parabolas. g ( x ) = 3x 2 - ...

Sketch the graph parabolas. g ( x ) = 3x 2 - 6 x + 5 Solution For this parabola we've obtain a = 3 , b = -6 and c = 5 .  Ensure that you're cautious with signs while id

Scientific notation, The average U.S. citizen consumes about 2.5 × 102 L of...

The average U.S. citizen consumes about 2.5 × 102 L of water per day for various uses. In 2013, there were about 3.16 × 108 U.S. citizens. About how many kiloliters of water were c

Need of rational root theorem, For starters it will let us to write down a ...

For starters it will let us to write down a list of possible rational zeroes for a polynomial and more significantly, any rational zeroes of a polynomial will be in this list. I

Determing slopes, Give the slope of each line and determine whether the 2 l...

Give the slope of each line and determine whether the 2 lines are parallel, perpendicular or neither: 4x+3y=9 and -9x+12y=0

New math, What is the effectiveness of new math?

What is the effectiveness of new math?

Negatives and positives, P=positive N=negative whats a negative - negative ...

P=positive N=negative whats a negative - negative p+n= n-n=

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd