SOLUTION: Consider the equation y=1 if x is rational 0 if x is irrational Answer the following What is the domain What is its range Is it even. odd, o

Question 1139600: Consider the equation y=1 if x is rational
0 if x is irrational
Answer the following

What is the domain
What is its range
Is it even. odd, or neither
Need each step explained in detail line by line step by step
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
The domain is all real numbers
:
The range is y=0, y=1
:
This is a discontinuous function, the graph would be just "dots" at either y = 0 or at y = 1.
:
This is an "even" function, because the negative of any positive rational would have a corresponding y value of 1 and the negative of any positive irrational would have a corresponding y value of 0. Thus, f(x) = f(-x).
:
The y intercept would be the "dot" at (0, 1) - because 0 is rational.
:
The "x" intercepts would just be the "dots" where the irrational numbers are located on the number line because "f(x)" would be 0 at those points.
:

RELATED QUESTIONS
Let y = piecewise function. Top portion of y = 1 if x is rational. Bottom... (answered by math_tutor2020)

Determine whether the following relation represents a function. If it is a function,... (answered by josgarithmetic,Theo)

I need to know what the vertex, axis of symmetry, roots, domain, and rang is for the... (answered by josgarithmetic)

Is the following sum rational or irrational? rational... (answered by Alan3354,ikleyn)

What is the domain of the following rational function? F(x)= ___ x+1___ (answered by ikleyn)

Can an irrational number raised to an irrational power yield an answer that is rational?... (answered by ikleyn)

y=1 if x is rational and y=0 if x irrational. how would you describe this on a... (answered by ikleyn)

Sketch the graph of a function for which the domain is all values of X and the rang is -2 (answered by Fombitz)

Domain x 0, 1, 2, 3 Domain y 0, .5, 2, 4.5 What is the rule? (answered by josgarithmetic)