The world’s largest snowman was higher than a 12-story building. One story is equivalent to 11 feet tall. How many inches high was the snowman? (Hint: 1 foot = 12 inches).
The graph of y=log(x-4) has a vertical asymptote at x = -4.
A. True
B. False
The correct answer and explanation is :
Part 1: Snowman Height Calculation
We are told that the world’s largest snowman was taller than a 12-story building. Each story is equivalent to 11 feet in height. To calculate the snowman’s height in inches, we need to first determine the total height in feet, then convert that into inches.
Step 1: Calculate the total height in feet
- Height of one story = 11 feet
- Number of stories = 12
Thus, the total height of the snowman in feet is:
[
\text{Total Height (in feet)} = 12 \, \text{stories} \times 11 \, \text{feet per story} = 132 \, \text{feet}
]
Step 2: Convert the height from feet to inches
Since 1 foot equals 12 inches, we multiply the height in feet by 12 to convert it to inches:
[
\text{Total Height (in inches)} = 132 \, \text{feet} \times 12 \, \text{inches per foot} = 1584 \, \text{inches}
]
So, the snowman was 1584 inches tall.
Part 2: Vertical Asymptote of ( y = \log(x-4) )
The function in question is ( y = \log(x – 4) ). To understand its behavior, we need to examine the equation and its domain:
The logarithmic function ( \log(x – 4) ) is defined only when the argument ( x – 4 ) is greater than zero. This means that:
[
x – 4 > 0 \quad \Rightarrow \quad x > 4
]
Thus, the domain of the function is ( x > 4 ), and the function is undefined for ( x \leq 4 ). The graph of ( y = \log(x – 4) ) has a vertical asymptote at ( x = 4 ) because as ( x ) approaches 4 from the right (i.e., from values greater than 4), the function values approach negative infinity. The function approaches positive infinity as ( x ) moves further to the right.
Since the problem statement says that the vertical asymptote is at ( x = -4 ), this is false. The correct vertical asymptote is at ( x = 4 ), not ( x = -4 ).
Thus, the correct answer is:
B. False
Summary:
- The snowman was 1584 inches tall, calculated by first determining its height in feet and then converting it to inches.
- The function ( y = \log(x – 4) ) has a vertical asymptote at ( x = 4 ), not ( x = -4 ), so the statement is false.