Sign Charts
Sign charts are graphical tools used in mathematics to analyze the behavior of polynomial functions. They provide a concise way to understand the sign of a function within specific intervals. By examining the intervals where the function is positive, negative, or zero, sign charts aid in identifying critical points, determining the behavior of a function, and finding the roots of equations. Through a systematic approach, sign charts streamline the process of understanding the overall behavior of functions without the need for exhaustive calculations, making them a valuable tool in algebraic analysis and problem-solving.
Questions
- How do you solve #1/2x^2>=4-x# using a sign chart?
- How do you solve #x^2+x-6<0# using a sign chart?
- Suppose #0< a,b,c < 1# and #ab + bc + ca = 1#. Find the minimum value of #a + b + c + abc#?
- How do you solve #(x+3)^2/x<=0# using a sign chart?
- How do you solve #x-10/(x-1)>=4# using a sign chart?
- Given the following functions; u(x) = x^2+9 w(x) = #sqrt(x+8)# How does one determine (w#@#u)(8) and (u#@w#)(8)?
- How do solve #x-10/(x-1)>=4# algebraically?
- How do you solve #(3-x)/(x+5)<=0# using a sign chart?
- How do you solve #x^3<=4x^2+3x# using a sign chart?
- How do solve #1/4<7/(7-x)# algebraically?
- How do you solve and graph #4x^4+36>=13x^2#?
- How do you solve #(x-2)/(x+4)<=0# using a sign chart?
- How do you solve #y^2-3y-9<=0# using a sign chart?
- How do you prove this equality #sqrt(3+sqrt(3)+(10+6sqrt(3))^(2/3))=sqrt(3)+1# ?
- How do you solve #(t-3)/(t+6)>0# using a sign chart?
- How do you solve #16-x^2>0# using a sign chart?
- How do you solve and graph #x^2+1<2x#?
- How do solve #5/x>3# and write the answer as a inequality and interval notation?
- How do solve #(x-4)/(x^2+2x)<=0# and write the answer as a inequality and interval notation?
- How do you solve #z^2-16<0# using a sign chart?