The table shows the relationship between the height of a tomato plant and the number of days since it has been planted
days height (cm)
2 3
5 4
8 6
12 9
18 13
22 15
25 16
30 20
32 21
35 24
what does the y-intercept represent in this problem situation? explain your answer.

The y-intercept represent Height

Step-by-step explanation:

In a graph the independent variable is plotted on the  X axis and attain only certain discrete values. The Dependent variable is plotted against the Y axis and may be discrete or continuous.

Here in the given question

Days:    2,5,8,12,18,22,25,30,32,35

Height: 3,4,6,9,13,15,16,20,21,24

The height is a dependant variable because we are trying to determine a relationship between the Days and the height. In particular, we are trying to see how the height depends upon what day it is or what is the height of the pant on the particular day.

The day can be only discrete values where height can be both discrete and continuous.

So height can be represented along Y axis

Step-by-step explanation:

The relation that the problem shows is between Days (x) and Height (y).

Remember that a y-incercept is a point with the form (0, k), where k is a real number.

In this case, the y-intercept represents the height of a tomato plant at day zero. In other words, it represents the initial condition, the height at the beginning of the experiment.

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!