Algebraic Set Query: Can a Take Any Value?

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In the equation a=bx, where x is a non-zero real constant and b can take any value, a can indeed take any value as well. The discussion emphasizes that when x is not equal to zero, varying b allows a to assume all real values. However, if x equals zero, a will always be zero regardless of b. The graph illustrates this relationship, confirming that the output a is dependent on the value of b when x is non-zero. Thus, the conclusion is that a can take any value as long as x is not zero.
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If a=bx, where x is a real constant and b can take literally any value, can a always take literally any value?
 
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Draw the graph (for x != 0) and tell us what you think.
 
OK fine, that's a trivial case. a=0 if x=0 regardless of b. For all x where x is not equal to 0?
 
Big-Daddy said:
If a=bx, where x is a real constant and b can take literally any value, can a always take literally any value?

Yes, as long as x is not 0.
 

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