(a) The number of jars j is the independent variable and the number of tomatoes t is the dependent variable.
(b) The equation is a linear function.
(c) The relationship is continuous.
(d) The input-output table is:
j 0 1 2 3 4
t 24 16 8 0 - 8
The function t(j) = - 8j + 24 represents the total number of tomatoes that the neighbor has left after producing j number of homemade salsa.
(a) The independent variable from the function is j the number of jars and the dependent variable is t or the number of tomatoes.
(b) Consider the function,
t(j) = - 8j + 24
As there is a constant rate of change ( 8 tomatoes for every 1 jar). Therefore, the equation is a linear function.
(c) The relationship is continuous because we can make it of a jar of salsa.
(d) Now, the function:
t(j) = - 8j + 24
When j = 0,
t(0) = - 8(0) + 24 = 24
When j = 1,
t(1) = - 8(1) + 24 = 16
When j = 2,
t(2) = - 8(2) + 24 = - 16 + 24 = 8
When j = 3,
t(3) = - 8(3) + 24 = -24 + 24 = 0
When j = 4,
t(4) = - 8(4) + 24 = - 32 + 24 = - 8
So, the input-output table is:
j 0 1 2 3 4
t 24 16 8 0 - 8
Learn more about function here:
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The complete question is mentioned below:
The function t(j) = - 8j + 24 represents the number of tomatoes t that your neighbor has left after making j jars of homemade salsa
(a) Identify the independent and dependent variables.
(b) Is this a linear function? Justify your answer.
(c) Is this relationship discrete or continuous? How do you know?
(d) Make an input-output table of possible values for the function.
(e) Graph the relationship. Be sure to label your axes.
