Question

I WILL MARK

Q. 7
The graph shows the rational function f (x) and the logarithmic function g(x).

Rational function f of x with one piece decreasing from the left in quadrant 3 asymptotic to the line y equals negative 6 and passing through the point negative 7 comma negative 8 and going to the right asymptotic to the line x equals negative 4 and another piece decreasing from the left in quadrant 2 asymptotic to the line x equals negative 4 and passing through the point negative 3 comma 0 and going to the right asymptotic to the line y equals negative 6 and a logarithmic function g of x increasing from the left in quadrant 3 asymptotic to the line y equals negative 4 passing through the point negative 3 comma 0 to the right

Which of the following feature(s) do the graphs of f (x) and g(x) have in common?

x-intercept
end behavior
vertical asymptote
A. I only
B. I and II only
C. I and III only
D. I, II, and III

Answer 1

C. I and III only.

Explanation:

Based on the given description of the graphs, both the rational function f(x) and the logarithmic function g(x) have the following features in common:

I. x-intercept: Both graphs pass through the point (-3, 0).

II. End behavior: The rational function f(x) has asymptotes at y = -6 and x = -4, while the logarithmic function g(x) has an asymptote at y = -4.

III. Vertical asymptote: The rational function f(x) has a vertical asymptote at x = -4.

Therefore, the correct answer is option C. I and III only.