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

Answer 1

See joint picture.

Explanation:

The study lasts 6 days. Since the amount of plant food decreased an equal amount each day, and since the whole 72 millimeters were used, it means that plants consumed 72/6 = 12 millimeters daily.

All the results given come from this justification.

Answer 2

The table and graph should be completed as shown in the image attached below.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + c

Where:

• m is the slope or rate of change.
• x and y are the points.
• c is the y-intercept or initial value.

Based on the information provided about this puppy, we have the following slope and y-intercept;

Slope, m = (0 - 72)/6 = -12

y-intercept, c = 72 (initial amount of plant food).

By substituting these parameters, an equation that models the weight of this puppy at the end of each week is given by;

y = mx + c

y = -12x + 72

In this context, a table that shows the relationship between the amount of plant food remaining, f(x), and the number of days that have passed should be completed as follows;

x function rule f(x)

0 y = -12(0) + 72 72

1 y = -12(1) + 72 60

2 y = -12(2) + 72 48

3 y = -12(3) + 72 36

4 y = -12(4) + 72 24

5 y = -12(5) + 72 12

6 y = -12(6) + 72 0