Question
Which function would vertically compress the function k(x)=2x−1−−−−−√+3
by a factor of 12
?(1 point)
Responses
b(x)=1.52x−1−−−−−√+3
b left parenthesis x right parenthesis equals 1.5 Start Root 2 x minus 1 End Root plus 3
j(x)=22x−1−−−−−√+3
b left parenthesis x right parenthesis equals 2 Start Root 2 x minus 1 End Root plus 3
m(x)=0.52x−1−−−−−√+3
m left parenthesis x right parenthesis equals 0.5 Start Root 2 x minus 1 End Root plus 3
c(x)=x−1−−−−−√+3
by a factor of 12
?(1 point)
Responses
b(x)=1.52x−1−−−−−√+3
b left parenthesis x right parenthesis equals 1.5 Start Root 2 x minus 1 End Root plus 3
j(x)=22x−1−−−−−√+3
b left parenthesis x right parenthesis equals 2 Start Root 2 x minus 1 End Root plus 3
m(x)=0.52x−1−−−−−√+3
m left parenthesis x right parenthesis equals 0.5 Start Root 2 x minus 1 End Root plus 3
c(x)=x−1−−−−−√+3
Answers
GPT-4o mini
To vertically compress the function \( k(x) = \sqrt{2x - 1} + 3 \) by a factor of \( 12 \), you need to multiply the original function by \( \frac{1}{12} \).
The function becomes:
\[
b(x) = \frac{1}{12} (\sqrt{2x - 1}) + 3
\]
However, if we look through the given options, they represent different transformations on \( k(x) \).
1. \( b(x) = 1.5\sqrt{2x - 1} + 3 \) (this is a vertical stretch, not a compression)
2. \( j(x) = 2\sqrt{2x - 1} + 3 \) (this is also a vertical stretch)
3. \( m(x) = 0.5\sqrt{2x - 1} + 3 \) (this compresses the function, but not by a factor of 12)
4. \( c(x) = \sqrt{2x - 1} + 3 \) (this is the original function)
None of the options explicitly show a vertical compression by a factor of \( 12 \).
To achieve a vertical compression by a factor of \( 12 \), the coefficient in front of the square root should be \( \frac{1}{12} \):
Thus, the correct answer based on the definition of vertical compression would be a function of the form:
\[
b(x) = \frac{1}{12}\sqrt{2x - 1} + 3
\]
However, since this option isn't present, the closest option that represents some kind of compression (though not the specified factor of \( 12 \)) is:
- **m(x) = 0.5\sqrt{2x - 1} + 3**, which compresses by a factor of \( 2 \).
But it's important to note that none of the given options compress the function by a factor of \( 12 \). Depending on your context, m(x) might be the best choice, despite it not being exactly what you're looking for.
The function becomes:
\[
b(x) = \frac{1}{12} (\sqrt{2x - 1}) + 3
\]
However, if we look through the given options, they represent different transformations on \( k(x) \).
1. \( b(x) = 1.5\sqrt{2x - 1} + 3 \) (this is a vertical stretch, not a compression)
2. \( j(x) = 2\sqrt{2x - 1} + 3 \) (this is also a vertical stretch)
3. \( m(x) = 0.5\sqrt{2x - 1} + 3 \) (this compresses the function, but not by a factor of 12)
4. \( c(x) = \sqrt{2x - 1} + 3 \) (this is the original function)
None of the options explicitly show a vertical compression by a factor of \( 12 \).
To achieve a vertical compression by a factor of \( 12 \), the coefficient in front of the square root should be \( \frac{1}{12} \):
Thus, the correct answer based on the definition of vertical compression would be a function of the form:
\[
b(x) = \frac{1}{12}\sqrt{2x - 1} + 3
\]
However, since this option isn't present, the closest option that represents some kind of compression (though not the specified factor of \( 12 \)) is:
- **m(x) = 0.5\sqrt{2x - 1} + 3**, which compresses by a factor of \( 2 \).
But it's important to note that none of the given options compress the function by a factor of \( 12 \). Depending on your context, m(x) might be the best choice, despite it not being exactly what you're looking for.