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?

Question

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.