To analyze the two functions and the statements, let's begin by determining the y-intercept and the rate of change for each function.
Function 1: The table provides the total cost (y) for given hours (x):
- For 0 hours: $45
- For 1 hour: $75
- For 2 hours: $105
- For 3 hours: $135
From this, we can calculate the y-intercept and rate of change:
- The y-intercept (when x = 0): $45
- Rate of change:
- From the table, the total cost increases by $30 for each additional hour (for example, from 0 to 1 hour the cost increases from $45 to $75, which is an increase of $30).
Function 2: The function is described as charging a flat rate of $50 and adding $40 for each hour worked:
- The cost function can be expressed as: \( y = 50 + 40x \)
From this function:
- The y-intercept (when x = 0): $50
- Rate of change: The rate of change is the coefficient of x which is $40 (the cost increases by $40 for each additional hour).
Now we can evaluate the statements:
-
Function 2 has a greater y-intercept than function 1.
- True. (Function 2's y-intercept is $50, which is greater than Function 1's $45.)
-
Function 1 has a greater rate of change than function 2.
- False. (Function 1's rate of change is $30; Function 2's is $40.)
-
Function 2 has a greater rate of change than function 1.
- True. (Function 2's rate of change is $40, which is greater than Function 1's $30.)
-
Function 1 has a greater y-intercept than function 2.
- False. (Function 1's y-intercept is $45, which is less than Function 2's $50.)
Summary of True Statements:
- Function 2 has a greater y-intercept than function 1.
- Function 2 has a greater rate of change than function 1.
1 answer