What is a fact about absolute value?
The absolute value of x is always either positive or zero, but never negative. From an analytic geometry point of view, the absolute value of a real number is that number’s distance from zero along the real number line. The absolute value of the difference of two real numbers is the distance between them.
What do absolute value equations do?
In an absolute value equation, an unknown variable is the input of an absolute value function. If the absolute value of an expression is set equal to a positive number, expect two solutions for the unknown variable. An absolute value equation may have one solution, two solutions, or no solutions.
What is special about absolute value functions?
An absolute value function is a function that contains an algebraic expression within absolute value symbols. Recall that the absolute value of a number is its distance from 0 on the number line. To graph an absolute value function, choose several values of x and find some ordered pairs.
How many solutions do absolute value equations have?
two solutions
Why do absolute value equations have two solutions?
Why are there two solutions to absolute value equations?
Has two solutions x = a and x = -a because both numbers are at the distance a from 0. An absolute value equation has no solution if the absolute value expression equals a negative number since an absolute value can never be negative.
How do you evaluate absolute values?
To evaluate an expression which contains an absolute value, first carry out the expression inside the absolute value sign according to the order of operations. Next, take the absolute value of the resulting number.
Absolute value equations have two solutions. Plug in known values to determine which solution is correct, then rewrite the equation without absolute value brackets.
What are the characteristics of an absolute value equation?
An absolute value equation is an equation having the absolute value sign and the value of the equation is always positive . The graph of the parent function of an absolute value equation is a v-shaped graph starting from the origin above the x-axis and rising both sides of the y-axis and is symmetrical to the y-axis.
How do you write an absolute value function?
The absolute value parent function, written as f( x )=| x | , is defined as. f( x )={ x if x>0 0 if x=0 −x if x<0. To graph an absolute value function, choose several values of x and find some ordered pairs.