Question

In addition to knowing the rate of change of a function, it is useful to know the starting value. What is the starting value of a function?

Check all that applies.


The starting value of a function is at (0,0).


The starting value is the output of the function when the input has a value of 0.


The starting value is (0, b), where b is the y-value when x is at 0.


The starting value of a function is when y=0.

Answer 1

To determine the correct statements about the starting value of a function, let’s analyze each one:

1. **The starting value of a function is at (0,0).**
- **False.** While the point (0,0) represents the output of the function when the input is 0 for the specific case of the function f(0) = 0, the starting value can vary depending on the function.

2. **The starting value is the output of the function when the input has a value of 0.**
- **True.** The starting value is indeed the output of the function when the input (x) is 0, which can be represented as f(0).

3. **The starting value is (0, b), where b is the y-value when x is at 0.**
- **True.** This statement essentially repeats the idea in the second statement, indicating that the output when x is 0 is what defines the starting value at the point (0, b).

4. **The starting value of a function is when y=0.**
- **False.** The starting value refers specifically to the output when the input is 0, not necessarily when y is 0. A function can have a starting output that is not 0.

In summary, the correct statements about the starting value of a function are:

- The starting value is the output of the function when the input has a value of 0.
- The starting value is (0, b), where b is the y-value when x is at 0.