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How do you find all the values that make the expression undefined: #(3z^2 + z)/(18z + 6)#?

Answer 1

Julia Adams

#z="no value"#

If you were to take the function as it is, then #18z+6!=0# #18z!=-6# #z!=-6/18=-1/3#

However, we can simplify the function: #(z(3z+1))/(6(3z+1))#

#(zcancel((3z+1)))/(6cancel((3z+1)))=z/6# and therefore all values will be defined.

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Answer 2

Abigail Allen

To find the values that make the expression undefined, we need to identify the values of z that would result in a denominator of zero. In this case, the expression is undefined when the denominator, 18z + 6, equals zero. Solving the equation 18z + 6 = 0, we find that z = -1/3. Therefore, the value -1/3 makes the expression undefined.

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Answer 3

Hazel Anglin

To find all the values that make the expression undefined, you set the denominator equal to zero and solve for ( z ). In this case, the denominator is ( 18z + 6 ). Setting it equal to zero gives ( 18z + 6 = 0 ). Solving for ( z ) yields:

[ 18z + 6 = 0 ] [ 18z = -6 ] [ z = \frac{-6}{18} ] [ z = -\frac{1}{3} ]

So, the expression is undefined when ( z = -\frac{1}{3} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.