Final answer:
To find the y-intercept of the piecewise function, we use the first piece '5x - 3' since it includes x = 0. Substituting x = 0 gives us the y-intercept at the point (0, -3).
Step-by-step explanation:
To find the y-intercept of a piecewise function, you should look at the piece of the function where x = 0, since the y-intercept occurs where a function crosses the y-axis. For the given function f(x) = {5x - 3 if x < 3, x² + 5 if 3 ≤ x < 10, 3 if x ≥ 10}, we use the first piece, which is 5x - 3, because it covers the range when x is less than 3, and this includes x = 0.
So, to find the y-intercept, we substitute x = 0 into the first piece of the function:
f(0) = 5(0) - 3 = -3
The y-intercept of the function f(x) is the point (0, -3).