Question

answer the following questions for the graph of (y = -5 log x).

a. what is the x-intercept? write in point form. write dne if the point does not exist.

b. what is the y-intercept? write in point form. write dne if the point does not exist.

c. draw the graph. there is a large margin for error for the graph. you just need the general shape of the graph.

Explanation:

Step1: Find the x-intercept

$$0 = -5 \log x \implies \log x = 0 \implies x = 10^0 = 1$$

Step2: Find the y-intercept

$$y = -5 \log(0) \implies \text{undefined} \implies \text{DNE}$$

Step3: Determine the graph shape

$$\lim_{x \to 0^+} -5 \log x = \infty, \quad \lim_{x \to \infty} -5 \log x = -\infty$$

Answer:

A. \((1, 0)\)
B. DNE
C. The graph of \(y = -5 \log x\) starts near the positive y-axis (as \(x \to 0^+\), \(y \to \infty\)), passes through the x-intercept at \((1, 0)\), and decreases gradually into the fourth quadrant as \(x\) increases (for example, passing through \((5, -3.5)\)).