Definition
Initial value
The initial value of a function is the output paired with an input of 0.
What it means
Start in the input column and look for 0. The output in the same row is the initial value. On the graph, the same input-output pair sits on the vertical axis because its x-coordinate is 0.
Remember it
Input 0 points to the starting output.
Example
For h(x) = 2x + 3, h(0) = 2 × 0 + 3 = 3. The table row is (0, 3), and the graph passes through (0, 3), so the initial value is 3.
Watch for
If 0 is not an allowed input, f(0) is not defined, so this input-zero sense of initial value does not exist for that function.
Common mix-up
The initial value is not necessarily the first row displayed in a table. It is the output at input 0, even when that row is shown later or must be worked out.
Exact meaning
For a function whose domain includes 0, the initial value is f(0), the output paired with input 0. On a coordinate graph it is the y-coordinate of the point with x = 0; for a linear rule y = mx + b, it is b.