Question
Write an equation for a function that has a graph with the given characteristics.
The shape of yequals=StartAbsoluteValue x EndAbsoluteValuex, but shifted left 22 units and up 55 units.
Question content area bottom
Part 1
Which of the following is the equation of the function?
A.y equals StartAbsoluteValue x plus 2 EndAbsoluteValue minus 5
y equals StartAbsoluteValue x plus 2 EndAbsoluteValue minus 5y=x+2−5
B.y equals StartAbsoluteValue x minus 2 EndAbsoluteValue plus 5
y equals StartAbsoluteValue x minus 2 EndAbsoluteValue plus 5y=x−2+5
C.y equals StartAbsoluteValue x plus 2 EndAbsoluteValue plus 5
y equals StartAbsoluteValue x plus 2 EndAbsoluteValue plus 5y=x+2+5
D.y equals StartAbsoluteValue x minus 2 EndAbsoluteValue minus 5
y equals StartAbsoluteValue x minus 2 EndAbsoluteValue minus 5y=x−2−5
The shape of yequals=StartAbsoluteValue x EndAbsoluteValuex, but shifted left 22 units and up 55 units.
Question content area bottom
Part 1
Which of the following is the equation of the function?
A.y equals StartAbsoluteValue x plus 2 EndAbsoluteValue minus 5
y equals StartAbsoluteValue x plus 2 EndAbsoluteValue minus 5y=x+2−5
B.y equals StartAbsoluteValue x minus 2 EndAbsoluteValue plus 5
y equals StartAbsoluteValue x minus 2 EndAbsoluteValue plus 5y=x−2+5
C.y equals StartAbsoluteValue x plus 2 EndAbsoluteValue plus 5
y equals StartAbsoluteValue x plus 2 EndAbsoluteValue plus 5y=x+2+5
D.y equals StartAbsoluteValue x minus 2 EndAbsoluteValue minus 5
y equals StartAbsoluteValue x minus 2 EndAbsoluteValue minus 5y=x−2−5
Answers
Answered by
GPT-4o mini
To create a function that has the shape of \( y = |x| \), but shifted left by 22 units and up by 55 units, we will apply the appropriate transformations to the absolute value function.
1. **Shifting Left by 22 Units**: To shift the graph of \( y = |x| \) left by 22 units, we replace \( x \) with \( x + 22 \). Thus, the equation becomes:
\[
y = |x + 22|
\]
2. **Shifting Up by 55 Units**: To shift the graph up by 55 units, we add 55 to the entire function. Therefore, the equation now becomes:
\[
y = |x + 22| + 55
\]
Now, let's compare our derived function \( y = |x + 22| + 55 \) with the offered options:
- **A**: \( y = |x + 2| - 5 \) (this does not match)
- **B**: \( y = |x - 2| + 5 \) (this does not match)
- **C**: \( y = |x + 2| + 5 \) (this does not match)
- **D**: \( y = |x - 2| - 5 \) (this does not match)
None of these options match the derived equation.
Upon reviewing the final adjustment of left and up transformations, the transformations indeed lead us to the final equation \( y = |x + 22| + 55 \).
If you need an answer from the existing options as they are, check if the options given might be incorrect. If there's an error or additional context leading to those options, please double-check or provide further clarification. Otherwise, none of the choices A-D are correct based on the shifts described.
1. **Shifting Left by 22 Units**: To shift the graph of \( y = |x| \) left by 22 units, we replace \( x \) with \( x + 22 \). Thus, the equation becomes:
\[
y = |x + 22|
\]
2. **Shifting Up by 55 Units**: To shift the graph up by 55 units, we add 55 to the entire function. Therefore, the equation now becomes:
\[
y = |x + 22| + 55
\]
Now, let's compare our derived function \( y = |x + 22| + 55 \) with the offered options:
- **A**: \( y = |x + 2| - 5 \) (this does not match)
- **B**: \( y = |x - 2| + 5 \) (this does not match)
- **C**: \( y = |x + 2| + 5 \) (this does not match)
- **D**: \( y = |x - 2| - 5 \) (this does not match)
None of these options match the derived equation.
Upon reviewing the final adjustment of left and up transformations, the transformations indeed lead us to the final equation \( y = |x + 22| + 55 \).
If you need an answer from the existing options as they are, check if the options given might be incorrect. If there's an error or additional context leading to those options, please double-check or provide further clarification. Otherwise, none of the choices A-D are correct based on the shifts described.