Final answer:
The logarithmic function b(x) = 4log5(x+3)-1 is vertical.
Step-by-step explanation:
The question provided is in the context of mathematics, specifically algebra and logarithms. The equation given, b(x)=4log5(x+3)-1, is a function in which the independent variable x is within a logarithmic expression. In mathematics, particularly when dealing with equations of lines, the general form y = mx + b is used where m represents the slope and b the y-intercept. For a logarithmic function, characteristics such as the base of the logarithm, the coefficients, and the constants added or subtracted will determine the shape and position of the graph. The function b(x) = 4log5(x+3)-1 is a logarithmic function. It represents a vertical shift of 1 unit downwards and a horizontal shift of 3 units to the left compared to the standard logarithmic function y = log5(x).
The vertical axis represents the values of the function, while the horizontal axis represents the input values, or x.
Therefore, the function b(x) is vertical.