Question

NEED ANSWER ASAP

Analyze the graph below to identify the key features of the logarithmic function. (6 points)

The x‐intercept is x = −5, and the graph approaches a vertical asymptote at x = −6.
The x‐intercept is y = −5, and the graph approaches a vertical asymptote at y = −6.
The x‐intercept is x = 5, and the graph approaches a vertical asymptote at x = 6.
The x‐intercept is y = 5, and the graph approaches a vertical asymptote at y = 6.

Answer 1

The x intercept is lies at the midpoint of (-6 and -4

so

• x=-5 is the x intercept

And it's translation of logx

translated equation

• y=log(x+6) as log x has x intercept at 1

Now the vertical asymptote is at

• (x+6)=0
• x=-6

Option A

Answer 2

The x‐intercept is x = −5, and the graph approaches a vertical asymptote at x = −6

Explanation:

From inspection of the graph:

x-intercept is where the curve intercepts the x-axis → x = -5

y-intercept is where the curve intercepts the y-axis → y ≈ 0.75

An asymptote is a horizontal or vertical line which the curve gets infinitely close to, but never touches.

From the portion of the curve in the graph, it appears that the curve gets very close to but never touches:

• the vertical line x = -6
• the horizontal line x = 1

(However, without seeing a large portion of the graph, we cannot be sure, particularly for the horizontal asymptote).

Therefore, from the given solution options:

The x‐intercept is x = −5, and the graph approaches a vertical asymptote at x = −6