absolute valued function help?

Question

how do you make a table of values for this absolute valued function? I don't get it. please help

f(x) = |x-3|

Answer 1

f(x) is the same as y.

So pick an x value, and a negative version of that same value, do the math, find the absolute value of the result, and that'd be y.

For example,
x = 2
y = |-1| = 1
x = -2
y = |-5| = 5

And so on.

Answer 2

Equations regarding absolute values may well be problematical to unravel. besides the undeniable fact that, it facilitates to isolate the expression interior of actual the linked fee on one area and then wreck the end result into 2 equations, finding on in spite of if the expression interior of actual the linked fee is decrease than 0 or no longer. in this occasion, if we expect that the expression interior of actual the linked fee is damaging, we would replace actual the linked fee image with a series of parentheses and multiply it by employing -a million to indicate the replace in sign. Or we would merely stick the damaging sign exterior the parentheses rather, meaning the comparable ingredient. Then we would resolve the ensuing equation, additionally determining which values of y (and x) this actual equation applies: x = (-a million)(y + 5); given y + 5 < 0 If y + 5 < 0, then y < -5 and x > 0 fixing for y supplies y = -x - 5 We would further handle the case the place the expression interior of actual the values is theory to be nonnegative, yet this time we merely replace actual the linked fee sign with parentheses. because of the fact the expression containing actual the linked fee is already remoted on one area of the equation, the parentheses are redundant and we can drop them. If y + 5 ? 0, then y ? -5 and x ? 0 and x = y + 5 fixing for y, we get y = x - 5 it would be observed that even although x may well be seen a function of y, y can not be seen a function of x because of the fact for each fee of x different than x = 0, we get 2 achievable values of y. the answer will for this reason be y = x - 5 OR y = -x - 5 if x ? 0. the comparable concerns persist with while working with inequalities, different than while the inequality image factors in direction of the expression contained in actual the linked fee image, the equations are coupled with AND quite than OR. this may well be real in spite of if the is a strict one (< or >) or additionally includes equality (? or ?) construction an inequality by employing negating an equation (?) additionally adjustments the OR logical conjunction to an AND.

Answer 3

just put it into a piecewise function and think about the different possibilities you get when plugging in different numbers.
when x is greater than or equal to 3, you can stick to x-3 because you dont get any kind of negative number just using that basic equation.
when x is less than 3, you would get a negative number, so time to find something else. If you just reverse it and make it 3-x, thats the same as using Ix-3I for all values less than 3.
Your answer should look something like this:
{x-3 , x >= 3
{3-x , x < 3.

Answer 4

Just start plugging in values for x, evaluating the function, and writing down the result.

x......|x-3|
-3.....6
-2.....5
-1.....4
0......3
1......2
2......1
3......0
4......1
5......2
And so on.

Doug