Answer: y-intercept at (0, -1) and a vertical asymptote at x = -5.
Step-by-step explanation:
To find the intercepts and asymptote of the function h(x) = -log5(x + 5), we can analyze the behavior of the function.
1. Intercepts:
- To find the x-intercept, we set h(x) = 0 and solve for x. However, in this case, the function -log5(x + 5) does not intersect the x-axis because the logarithm of a negative number is undefined.
- To find the y-intercept, we evaluate h(x) when x = 0. Substituting x = 0 into the function, we get h(0) = -log5(0 + 5) = -log5(5) = -1.
2. Asymptote:
- The function h(x) = -log5(x + 5) has a vertical asymptote at x = -5. As x approaches -5 from the left, the function approaches negative infinity. As x approaches -5 from the right, the function approaches positive infinity.
- There is no horizontal asymptote in this case since the logarithm function does not have a horizontal asymptote.
In summary, the function h(x) = -log5(x + 5) has a y-intercept at (0, -1) and a vertical asymptote at x = -5.
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