Questions: Find the domain of the logarithmic function and then graph the function. y=ln(7x-6) Find the domain of the function. (6/7, ∞) (Type your answer in interval notation. Use integers or fractions for any numbers in the expression. Simplify your answer.) Graph the function. Choose the correct graph below.

Find the domain of the logarithmic function and then graph the function. y=ln(7x-6) Find the domain of the function. (6/7, ∞) (Type your answer in interval notation. Use integers or fractions for any numbers in the expression. Simplify your answer.) Graph the function. Choose the correct graph below.
Transcript text: Find the domain of the logarithmic function and then graph the function. \[ y=\ln (7 x-6) \] Find the domain of the function. \[ \left(\frac{6}{7}, \infty\right) \] (Type your answer in interval notation. Use integers or fractions for any numbers in the expression. Simplify your answer.) Graph the function. Choose the correct graph below.
failed

Solution

failed
failed

Solution Steps

Step 1: Find the domain of the logarithmic function

The logarithmic function is defined only for positive arguments. Therefore, to find the domain of _y_ = ln(7_x_ - 6), we must determine the values of _x_ for which 7_x_ - 6 > 0.

Solving the inequality: 7_x_ - 6 > 0 7_x_ > 6 _x_ > 6/7

So, the domain of the function is (6/7, ∞).

Step 2: Determine the correct graph

The graph of _y_ = ln(_x_) has a vertical asymptote at _x_ = 0 and passes through the point (1, 0). The graph of _y_ = ln(7_x_ - 6) is a horizontal translation of ln(_x_). The vertical asymptote shifts to _x_ = 6/7, which is approximately 0.86. Looking at the graphs, option A has a vertical asymptote slightly before 1, near 6/7, which makes it the correct graph.

Final Answer:

Domain: (6/7, ∞) Graph: A

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Cellular images of the cross-section of the stem of Tradescantia pallida
failedAnswered
Suppose that θ is an angle in standard position whose terminal side intersects the unit circle at (15/17, -8/17). Find the exact values of sin θ, sec θ, and cot θ. sin θ= sec θ= cot θ=
failedAnswered
Question 25, 3.4.19 HW Score: 49.46%, 16.82 of 34 Part 2 of 3 points Points: 0 of 1 The following graph is an ogive of a standardized test's (a) Find and interpret the percentile rank of a test scores. The vertical axis in an ogive is the cumulative relative frequency and can also be interpreted as a percentile. Complete parts a through c. score with a value of 130 A test score of 130 corresponds to the 50th percentile rank since this percentage of test scores are less than or equal to a test score with a value of 130. (b) Find and interpret the percentile rank of a test score with a value of 140. A test score of 140 corresponds to the percentile rank since this percentage of test scores are a test score with a value of 140.
failedAnswered
What in thin milt
failedAnswered
Why or how does this cause a problem? How can I avoid this problem in the future? Who can help me solve this problem? When is the ideal time to implement my solution?