Final answer:
Among the options given for a first-degree polynomial function that intercepts the vertical axis at 8, the correct function is a) f(x) = x + 8. This function has a y-intercept of 8, represented by the constant term in the linear equation.
Step-by-step explanation:
The question presented concerns a first-degree polynomial function, also known as a linear function, that intersects the vertical axis, which is the y-axis, at the point where the y-coordinate is 8. This point is referred to as the y-intercept of the graph. The y-intercept for any linear equation in the form of f(x) = mx + b is the value of b. Therefore, to find a function whose graph intercepts the vertical axis at 8, we look for the function where b is equal to 8.
Among the given options:
- Option a) f(x) = x + 8
- Option b) f(x) = x - 8
- Option c) f(x) = 8x
- Option d) f(x) = -8x
Only option a) f(x) = x + 8 correctly represents a function with a y-intercept of 8, as this equation implies that when x is 0, f(x) or y is equal to 8. Therefore, when the function crosses the vertical y-axis, it will do so at the point (0, 8).