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A Sign Chart is similar to a number line but includes certain numbers on the horizontal line. It helps to determine the sign, positive or negative, of a function between an interval. Sign Charts are useful to solve linear inequalities and graph functions. This article will provide the necessary information to correctly create a Sign Chart.
== Steps ==
# Write down the problem. Although it may seem redundant, writing down the problem is important in order to make reference to it easily.
# Find the critical numbers of the function given. Critical numbers are any x-(or any variable) values where the function is equal to zero. To find these values, set the function equal to zero and solve for x.
# Find the undefined numbers, if any, of the function given. Undefined numbers are the x-(or any variable_ values where these numbers break the domain of the function. To find these numbers, I consider my domain restrictions (any fraction cannot have a denominator equal to zero, the radicand of even indexed radical function cannot be negative, the inside of any logarithmic function cannot equal zero and cannot be negative), and solve for x according to the domain restrictions of the given function.
#* If the function contains a fraction, set the denominator of the function equal to zero and solve for x. However, because the denominator cannot be zero, the x-values found are written as x cannot equal to the values
#* If the function contains an even indexed radical expression, set the radicand greater than or equal to zero and solve for x
#* If the function contains a logarithmic expression, set the inside of the logarithm greater than or equal to zero and solve for x
# Make a straight horizontal line
# From left to right, in increasing order place the critical and undefined numbers on the straight line drawn
# Look at the left-most interval. By place the numbers in increasing order we have created intervals which will help to determine the signs of different numbers within these intervals.
# Choose a number. The number you choose should be less than, but not equal to, the critical/undefined value in the interval.
# Plug that number into the function given and simplify.
# Record the sign of the value found in the previous step. After simplify, the number you have determined will either be positive or negative. Within the interval, write down positive if the number you calculated was positive or negative if the number you calculated was negative.
# Look at the next interval to the immediate right of the left-most interval. Notice this interval should now be between two critical numbers and/or undefined numbers.
# Choose another number and repeat steps 8 and 9. The next number chosen should be between, but not equal to, the two critical and/or undefined numbers of the interval.
# Repeat step 10 and step 11. Steps 10 and 11 should be repeated until you reach the right-most interval.
# Look at the right-most interval and choose another number. This number should be greater than, but not equal to, the critical/undefined number in the interval.
# Repeat step 8 and step 9
== Tips ==
* When plugging in any number into a function, double check your algebra. If one thing is calculated wrong it could mess up the sign of the value
== Steps ==
# Write down the problem. Although it may seem redundant, writing down the problem is important in order to make reference to it easily.
# Find the critical numbers of the function given. Critical numbers are any x-(or any variable) values where the function is equal to zero. To find these values, set the function equal to zero and solve for x.
# Find the undefined numbers, if any, of the function given. Undefined numbers are the x-(or any variable_ values where these numbers break the domain of the function. To find these numbers, I consider my domain restrictions (any fraction cannot have a denominator equal to zero, the radicand of even indexed radical function cannot be negative, the inside of any logarithmic function cannot equal zero and cannot be negative), and solve for x according to the domain restrictions of the given function.
#* If the function contains a fraction, set the denominator of the function equal to zero and solve for x. However, because the denominator cannot be zero, the x-values found are written as x cannot equal to the values
#* If the function contains an even indexed radical expression, set the radicand greater than or equal to zero and solve for x
#* If the function contains a logarithmic expression, set the inside of the logarithm greater than or equal to zero and solve for x
# Make a straight horizontal line
# From left to right, in increasing order place the critical and undefined numbers on the straight line drawn
# Look at the left-most interval. By place the numbers in increasing order we have created intervals which will help to determine the signs of different numbers within these intervals.
# Choose a number. The number you choose should be less than, but not equal to, the critical/undefined value in the interval.
# Plug that number into the function given and simplify.
# Record the sign of the value found in the previous step. After simplify, the number you have determined will either be positive or negative. Within the interval, write down positive if the number you calculated was positive or negative if the number you calculated was negative.
# Look at the next interval to the immediate right of the left-most interval. Notice this interval should now be between two critical numbers and/or undefined numbers.
# Choose another number and repeat steps 8 and 9. The next number chosen should be between, but not equal to, the two critical and/or undefined numbers of the interval.
# Repeat step 10 and step 11. Steps 10 and 11 should be repeated until you reach the right-most interval.
# Look at the right-most interval and choose another number. This number should be greater than, but not equal to, the critical/undefined number in the interval.
# Repeat step 8 and step 9
== Tips ==
* When plugging in any number into a function, double check your algebra. If one thing is calculated wrong it could mess up the sign of the value
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