This equation means that the distance is 2, either in the positive direction or the negative direction.
|x-4|= 2 ⇒ lx-4= 2 x-4= -2
To find the solutions to the absolute value equation, we need to solve both of these cases for x.
Both (6,0) and (2,0) are x-intercepts of this function. Now we will find the y-intercept, the point where function intersects the y-axis. This time we are substituting 0 for x in the function rule.
Let's recall the general equation of the absolute value functions.
y= a|x- h|+ k
In this form the locator point is ( h, k). Now let's take a look at the given equation.
y=|x-4|-2 ⇒ y= 1|x- 4|+( -2)
Since the given function is in the general form, the locator point is ( 4, -2)
Domain and Range
The domain of an absolute value function will usually be all real numbers, unless specific restrictions have been imposed upon the function.
Domain: All real numbers
To find the range, we need to think about where the locator point of the function is situated. Because this type of function will always have the same basic V-shape, the y-value of this point is the minimum (if a>0) or maximum (if a<0) of the range. In this case a=1, so -2 is the minimum of the given function.
Range:y≥ -2
This equation means that the distance is 3, either in the positive direction or the negative direction.
|x+1|= 3 ⇒ lx+1= 3 x+1= -3
To find the solutions to the absolute value equation, we need to solve both of these cases for x.
Both (2,0) and (-4,0) are x-intercepts of this function. Now we will find the y-intercept, the point where function intersects the y-axis. This time we are substituting 0 for x in the function rule.
Let's recall the general equation of the absolute value functions.
y= a|x- h|+ k
In this form the locator point is ( h, k). Now let's take a look at the given equation.
y=-|x+1|+3 ⇒ y= -1|x-( -1)|+ 3
Since the given function is in the general form, the locator point is ( -1, 3)
Domain and Range
The domain of an absolute value function will usually be all real numbers, unless specific restrictions have been imposed upon the function.
Domain: All real numbers
To find the range, we need to think about where the locator point of the function is situated. Because this type of function will always have the same basic V-shape, the y-value of this point is the minimum (if a>0) or maximum (if a<0) of the range. In this case a=-1, so 3 is the maximum of the given function.
Range:y≤ 3
