Question

Find the domain and function of y=6+9x/6-|x-1|

Thank you so soooo much for the help!!

Answer 1

Answer is x < -5; -5 < x < 7; x > 7

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Step-by-step explanation:

Rule: We cannot divide by zero.

Because of that rule, we'll set the denominator equal to zero and solve for x. This way we can determine the x value(s) that are to be excluded from the domain.

6 - |x-1| = 0

|x-1| = 6

x-1 = 6 or x-1 = -6

x = 6+1 or x = -6+1

x = 7 or x = -5

Those x values are to be excluded from the domain, since they make the denominator zero.

Imagine a number line in which we poked open holes at -5 and 7

• The portion to the left of -5 is x < -5
• The portion between -5 and 7 is -5 < x < 7
• The portion to the right of 7 is x > 7

Combining everything gets us x < -5; -5 < x < 7; x > 7