28.2k views
5 votes
Find the (x , y) coordinate(s) of any hole(s) in h( x ). If there is none, write “n/a”.Round to two decimals.

Find the (x , y) coordinate(s) of any hole(s) in h( x ). If there is none, write “n-example-1
User Zinc
by
8.0k points

1 Answer

4 votes

The hole appears in the rational function when the numerator and the denominator have the same zeroes

Since the rational function is


h(x)=(x+7)/(x^2-49)

Factorize the denominator


x^2-49=(x+7)(x-7)

The rational function h(x) is


h(x)=(x+7)/((x+7)(x-7))

Since (x + 7) is in both numerator and denominator

Then there is a hole at x + 7 = 0

Let us find the value of x


\begin{gathered} x+7=0 \\ x+7-7=0-7 \\ x=-7 \end{gathered}

The whole is at x = -7

Then simplify the fraction to find the value of y at x = -7


h(x)=((x+7))/((x+7)(x-7))

Cancel the bracket (x+7) up by the same bracket down


h(x)=(1)/(x-7)

Substitute x by -7


\begin{gathered} h(-7)=(1)/(-7-7) \\ h(-7)=(1)/(-14) \\ y=-(1)/(14) \end{gathered}

The hole is at (-7, -1/14)

User Edy Aguirre
by
7.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories