function A is a straight line Function B: Function C: y=x+5

Question

that is plotted at (-4, 0) x y
(-2, 1) (0, 2) 0 3
(2, 3) 4 -9
8 -21
(4 points)
Which function has a negative rate of change (slope)?

Which function has the smallest y-intercept?

Which function would you want to represent your money earned per hour?

Which function would give you the highest initial amount of money?

Answer 1

To analyze the given functions, we can start by considering the pattern and characteristics of each function, based on the provided information.

1. Function A: Plotted points at (-4, 0), (-2, 1), and (2, 3) indicate it is a straight line. To determine its slope, we can use the change in y over the change in x (rise/run). Between the points (-4, 0) and (2, 3):

   • Change in y = 3 - 0 = 3
   • Change in x = 2 - (-4) = 6
   • Slope (m) = Change in y / Change in x = 3 / 6 = 1/2 (positive slope).

2. Function B: It is a table of values:

   x | y
   ------
   0 | 3
   4 | -9
   8 | -21
   

   Looking at the values:

   • From 0 to 4: y goes from 3 to -9 (decreases of 12 in y)
   • From 4 to 8: y goes from -9 to -21 (decreases by 12 again)

   The rate of change is negative as y decreases when x increases, suggesting a negative slope.

3. Function C: Represented by the equation \(y = x + 5\).

   • The slope is 1 (positive) since the coefficient of x is positive.
   • The y-intercept is 5 (when x = 0, y = 5).

Now we can answer the specific questions:

1. Which function has a negative rate of change (slope)?

   • Function B has a negative rate of change.

2. Which function has the smallest y-intercept?

   • The y-intercepts are as follows:
     • Function A has no clear y-intercept from the points directly because we don’t have an explicit equation.
     • Function B appears to have points well below 0 for x values greater than 0.
     • Function C has a y-intercept of 5.
     • Thus, Function B has the smallest y-intercept (which is less than 0).

3. Which function would you want to represent your money earned per hour?

   • You would want a function with a positive slope. Thus, Function C (y = x + 5) would be the most suitable choice as it indicates that money earned increases with each hour worked.

4. Which function would give you the highest initial amount of money?

   • The highest initial amount of money refers to the y-intercept when x = 0.
   • Function C has a y-intercept of 5, and Function B has values that start below 0.
   • Therefore, Function C would give you the highest initial amount of money.

In summary:

• Function with negative rate of change: Function B
• Function with the smallest y-intercept: Function B
• Function to represent money earned per hour: Function C
• Function with the highest initial amount of money: Function C

Answer 2

2nd question is function A the rest are correct.