Question

Graph the function rule. Tell whether the the graph is continuous or discrete. The height h, in inches, of the juice in a 20-oz bottle depends on the amount of juice j, in ounces, that you drink. This situation is represented by the function rule h=6-0.3j.

Answer 1

Answer:

The graph of our given function will be continuous.

Step-by-step explanation:

Please find the attached graph of our given function.

Let h represent the height in inches and j represent the amount of juice in ounces.

We have been given that the height of the juice in a 20-oz bottle depends on the amount of juice. This means that j in independent variable and h is dependent variable.

The function $h=6-0.3j$ represents the height of juice after drinking j ounces of juice.

As we drink the juice, the height of the juice in bottle will change continuously. The graph of our given function will be continuous as we can drink fractions of an ounce juice.

Since the equation of  line in slope-intercept form is $y=mx+b$, where,

m = Slope of line,

b= y-intercept or initial value.

Upon comparing our given function with slope-intercept form of equation we can see that slope of our given function is -0.3 and y-intercept is 6. Negative slope indicates that height of juice in bottle is decreasing after drinking  j ounces of juice.

In order to graph our line we need to find x-intercept, which will be at height equals 0 inches.

Upon substituting h = 0 in our given function we will get,

$0=6-0.3j$

$0+0.3j=6-0.3j+0.3j$

$0.3j=6$

$\frac{0.3j}{0.3}=\frac{6}{0.3}$

$j=20$

So let us draw a line from points (0,8) to (20,0).

Therefore, the line connecting to these points will be the line representing our given function.