\( h(x) \) has a hole or a vertical asymptote. Factored form: \( h(x)= \) \( \qquad \) Hole: \( \qquad \) \( \frac{(x+2)(x-2}{(x+12)(x+1} \) \( \qquad \) Vertical asymptote: rample 2: Find the domain of \( h(x) \) from Exam \[ (-\infty,-5)(-5,-2) \] Te 3: Let \( k(x)=\frac{x^{2}-x-12}{x^{3}+x^{2}-20 x} \). an equation for \( k(x) \) in factored form: \( \qquad \) \( y \) zeros of the function \( k(x) \) : values of \( x \) where \( k(x) \) has a hole: \( \qquad \) ertical asymptotes of \( k(x) \) :
Added by Kelsey R.
Close
Step 1
Given: \[ h(x) = \frac{(x+2)(x-2)}{(x+12)(x+1)} \] Show more…
Show all steps
Your feedback will help us improve your experience
Khushbu Rani and 67 other Algebra educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
In Exercises $1-6,$ find all values $x=a$ where the function is discontinuous. For each point of discontinuity, give (a) $f(a)$ if it exists, (b) $\lim _{x \rightarrow a^{-}} f(x), \lim _{x \rightarrow a^{+}} f(x),(\mathrm{d}) \lim _{x \rightarrow a} f(x),$ and $(\mathrm{e})$ identify which conditions for continuity are not met. Be sure to note when the limit doesn't exist.
The Derivative
Continuity
Find the vertical asymptotes, if any, and the values of $x$ corresponding to holes, if any, of the graph of each crational function. $$ h(x)=\frac{x+6}{x^{2}+2 x-24} $$
Polynomial and Rational Functions
Rational Functions and Their Graphs
Zhumagali S.
Recommended Textbooks
Elementary and Intermediate Algebra
Algebra and Trigonometry
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD