The function h(x) = -log base 5 of (x + 5) has intercepts at (-4, 0) and (0, -1), and its asymptote is a vertical line at x = -5.
The given function is h(x) = -log base 5 of (x + 5). To determine the intercepts and asymptote using the graph, we interpret the information provided.
x-Intercept: The curve crosses the x-axis 4 units to the left of the origin. To find this intercept, we set h(x) to zero and solve for x: 0 = -log base 5 of (x + 5). Solving this equation gives x = -4, so the x-intercept is (-4, 0).
y-Intercept: The curve crosses the y-axis one unit below the origin. Setting x to zero, we find h(0) = -log base 5 of (5) = -1, so the y-intercept is (0, -1).
Asymptote: The curve decreases rapidly following the vertical line 5 units to the left of the y-axis. This vertical line is a vertical asymptote for the function. In general, for a logarithmic function of the form -log base b of (x + c), the vertical asymptote is given by x = -c. Therefore, in this case, the asymptote is x = -5.
In summary, the intercepts of h(x) = -log base 5 of (x + 5) are (-4, 0) for the x-axis and (0, -1) for the y-axis. The asymptote is a vertical line at x = -5, five units to the left of the y-axis.