Domain and range for the absolute value equation: y = -30|x-6.5| + 105?

Question

PLEASE could you explain how you got the answers too? Thanks in advance for any assistance you can provide!

Answer 1

boy... you needs to do ur own hmwk!

Answer 2

Domain and range are the X and Y values that are covered by the graph. We know when we look at the equation that there are no values X cannot be meaning there is no place were it is undefined. Examples of undefined: division by zero, asymtope.
To find the range we know that the absolute value is shaped like a V. The vertex or the pointy part of the V shape is the end point for the Y values (The graph goes no higher in this case)
The answer will be D:(-inf,inf) (inf=infinity)
The range is (-inf,105] ()=means number not included [ ] is included.
We know the range because we know that the vertex of the orginal IXl graph is 0,0. The constants (numbers without variables) move the graph up and down (along the Y axis). The constant here was moved up 105.

Further Reference.
The numbers inside () or l l move the graph right and left, the opposite of their sign
For example (x+3) moves left 3 spaces!
Good luck

Answer 3

The domain is all possible x-values you could substitute for that variable. I think the domain, here, is infinite.

The range is all possible y-values that would result. Think about it: what would the answer be if you put in x=0?
X=some negative number?
X=some positive number?
Since the answer from (x-6.5) is an absolute value, it will always be a positive number that you're multiplying by negative 30. That means your answer from this multiplication will always be negative.

So what really makes a difference is the value you end up adding to the 105.

Hope this helps you out.

Answer 4

Domain: all real numbers (normally numbers are excluded for reasons such as division by zero, taking square root of a negative number, etc)
Range: |x - 6.5| >= 0 for any x, so -30|x-6.5| <= 0. Therefore y <= 105.