Question
Question
Which equation below shows the current graph if it were shifted 5 units down?
(1 point)
Responses
y=−12x+5
y is equal to negative 1 half x plus 5 - incorrect
y=−12x−7
y is equal to negative 1 half x minus 7 - no response given
y=−7
Which equation below shows the current graph if it were shifted 5 units down?
(1 point)
Responses
y=−12x+5
y is equal to negative 1 half x plus 5 - incorrect
y=−12x−7
y is equal to negative 1 half x minus 7 - no response given
y=−7
Answers
GPT-4o mini
To shift a graph down by 5 units, you would subtract 5 from the original equation.
If you take an equation of the form \( y = f(x) \), shifting it down by 5 would give you:
\[ y = f(x) - 5 \]
Now, let’s analyze the options given:
1. \( y = -12x + 5 \) shifted down by 5 gives \( y = -12x + 5 - 5 = -12x \). This is not listed in the options.
2. \( y = -\frac{1}{2}x + 5 \) shifted down by 5 gives \( y = -\frac{1}{2}x + 5 - 5 = -\frac{1}{2}x \). This is also not listed.
3. \( y = -12x - 7 \) shifted down by 5 gives \( y = -12x - 7 - 5 = -12x - 12\), which does not match any transformation provided.
4. \( y = -7 \) has no information about its transformation, but if shifted down by 5 (and its original was assumed to be \( y = -2 \)), it would become \( y = -7 - 5 = -12\).
Since none of the shifted graphs directly correspond to the form of their original state from what is given, unless you are specifying \( y = -2 \) originally for the last one, there is no clear answer among the provided options for a generic transformation.
It appears that without clarity on the original equations for the options, it's impossible to choose a shifted representation. Please verify the original equations for accuracy or provide them for correct results.
Among the options given, none directly indicate a correct transformation without additional information on their form before the shift.
If you take an equation of the form \( y = f(x) \), shifting it down by 5 would give you:
\[ y = f(x) - 5 \]
Now, let’s analyze the options given:
1. \( y = -12x + 5 \) shifted down by 5 gives \( y = -12x + 5 - 5 = -12x \). This is not listed in the options.
2. \( y = -\frac{1}{2}x + 5 \) shifted down by 5 gives \( y = -\frac{1}{2}x + 5 - 5 = -\frac{1}{2}x \). This is also not listed.
3. \( y = -12x - 7 \) shifted down by 5 gives \( y = -12x - 7 - 5 = -12x - 12\), which does not match any transformation provided.
4. \( y = -7 \) has no information about its transformation, but if shifted down by 5 (and its original was assumed to be \( y = -2 \)), it would become \( y = -7 - 5 = -12\).
Since none of the shifted graphs directly correspond to the form of their original state from what is given, unless you are specifying \( y = -2 \) originally for the last one, there is no clear answer among the provided options for a generic transformation.
It appears that without clarity on the original equations for the options, it's impossible to choose a shifted representation. Please verify the original equations for accuracy or provide them for correct results.
Among the options given, none directly indicate a correct transformation without additional information on their form before the shift.