Question

What is the Absolute value of -58 is
a) 58
b) -58
c) 0
d) None of these

Answer 1

Hint: First draw the graph of absolute value function, then try to find the intersection point at the given value. Then you can say the value of the function at the given point, this is the required result in the given question as absolute value.

Complete step-by-step answer:
Absolute value: In mathematics the absolute value is nothing but modulus. The absolute value of real number x, is the modulus of the real number x, which is denoted by $\left| x \right|$ . It is O for zero.
Method to draw the graph of $\left| x \right|$ : We know the graph of the equation given by y = x. By differentiating on both sides we get its values as
$\dfrac{dy}{dx}=1$
So, y = x is a straight line with the slope as 1.

Now we can apply modulus to x in the equation y = x. So, we say that when we apply modulus only to x in the equation by graphical properties, the graph turns as a reflection of x-axis while x is negative. If x is positive then the graph remains the same. By above we can say the graph of $y=\left| x \right|$ as

The graph of x = -58 is drawn as: Slope is infinity, so it is a straight line parallel to y-axis

By combining both the above graphs, we get it as,

The intersection point is (-58, 58). So, the absolute value of x = -58 is +58.

Note: Be careful while taking reflection, you must take only on the negative side as the positive side remains the same. Because modulus does not affect the positive number while getting an intersection you must point it carefully. Alternate method is to use modulus function
\[\left| x \right|=\left\{ \begin{matrix}
   x,x>0 \\
   0,x=0 \\
   -x,x<0 \\
\end{matrix} \right.\]
Substitute given value here to get a result. Anyways you get the same result here also.