Modeling/Reasoning task Directions: Show all of your work you do to find the answers. Even if you cannot answer all parts, answer as many as you can. You may still get points for answering part of the question.

Sara and Jake shared a chocolate bar. Jake teased Sara saying “I have 4/6 of the candy bar. You only have ⅔ of it. I have more than you.” Use words, number sentences, and the rectangle below to help Sara explain to Jake that they have the same amount of the candy bar.

the answer is the third / last answer

step-by-step explanation:

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation:

the domain of a function is the set of input values, x , for which a function is defined. the domain is shown in the left oval in the picture below. the function provides an output value, f(x) , for each member of the domain.