Question

Function representations in this activity, you will use multiple representations of relationships to identify key features and solve problems. ryan conducted a 6-day study observing the effects of an organic plant food on the growth of his sprouting bean plant. he tracked these two pieces of information: the amount of plant food remaining in the container after each day’s feeding the height of the plant over time part a ryan found that the amount of plant food remaining decreased an equal amount each day, and he used the entire 72 milliliters by the end of his study. question 1 question which statement is true about the relationship between the amount of plant food remaining and the number of days? this relationship is not a function because only one amount of plant food remains each day. this relationship is a function because more than one amount of plant food remains each day. this relationship is not a function because more than one amount of plant food remains each day. this relationship is a function because only one amount of plant food remains each day. question 2 question write a function rule for the relationship between the amount of plant food remaining, f(x), and the number of days that have passed, x. type the correct answer in the box. big fraction parentheses vertical bars square root root superscript (ctrl up) subscript (ctrl down) plus sign minus sign middle dot multiplication sign equals sign less-than sign greater-than sign less-than or equal to greater-than or equal to pi alpha beta epsilon theta lambda mu rho phi sine cosine tangent arcsine arccosine arctangent cosecant secant cotangent logarithm logarithm to base n natural logarithm bar accent right left arrow with under script right arrow with under script angle triangle parallel to perpendicular approximately equal to tilde operator degree sign intersection union summation with under and over scripts matrix with square brackets f(x)= question 3 question determine the domain and the range for this relationship. dra

Answer 1

The relationship is a function because there is a specific amount of plant food remaining for each day. The function rule is f(x) = 72 - 12x, and the domain and range are {0, 1, 2, 3, 4, 5, 6} and {72, 60, 48, 36, 24, 12, 0}, respectively.

Step-by-step explanation:

The relationship between the amount of plant food remaining and the number of days is a function because for each day, there is exactly one unique amount of plant food remaining. This characteristic satisfies the definition of a function. Given that Ryan used the entire 72 milliliters of plant food over 6 days with a uniform decrease in the amount of plant food each day, the function rule for the amount of plant food remaining, f(x), after x days would be:

f(x) = 72 - 12x

Here, 12 is the amount of plant food used per day, which results from dividing the total amount of plant food (72 ml) by the number of days (6 days).

The domain of this function consists of the days Ryan observed the plant growth, which would be {0, 1, 2, 3, 4, 5, 6}, assuming day 0 is the starting point and day 6 is the end. The range reflects the amount of plant food remaining and would be {72, 60, 48, 36, 24, 12, 0}.