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Parent functions an upward wide V shape (0,0), (-2,2),(2,2),(-3,3),(3,3)

The transformed function is an upward V shape but not as wide ((2,0),(1.5,4),(2.5,4)
The two branches of function B have steeper slopes and has shifted to right 2 units
Less steep slope and shifted to right 2 units
Has less steep slopes and shifted to left 2 units
Has steeper slopes and to left 2 units

3 answers

From your description, it seems you are working with transformations of the absolute value parent function \( f(x) = |x| \), which has the characteristic 'V' shape.

The parent function’s points you provided suggest the function is defined by:

  1. Parent function: \( f(x) = |x| \)
    • Points: (0,0), (-2,2), (2,2), (-3,3), (3,3)

The parent function opens upward with vertex at (0,0).

Considering the transformed function you mentioned:

  1. Transformed function: \( g(x) \) appears to be an absolute value function shifted to the right and is also less steep than the parent function, represented by the points (2,0), (1.5,4), (2.5,4).

To achieve the transformation you described, we might consider the following:

Transformations:

  • Horizontal shift to the right: This can be represented by a function like \( f(x - h) \) where \( h > 0 \) is the value of the shift.
  • Vertical stretch/compression: This involves multiplying the function by a factor \( a\). If \( 0 < a < 1 \), the graph becomes less steep (more wide), and if \( a > 1 \), the graph becomes steeper.

Transformation Analysis

Based on your observations:

  1. "The two branches of function B have steeper slopes and has shifted to right 2 units"

    • This suggests the function might look something like: \[ g(x) = a |x - 2| \] where \( a > 1 \).

  2. "Less steep slope and shifted to right 2 units"

    • Indicating that the transformation applies a decrease in steepness with a change similar to: \[ g(x) = a |x - 2| \] where \( 0 < a < 1\).

  3. "Has less steep slopes and shifted to left 2 units"

    • This indicates a function like: \[ g(x) = a |x + 2| \] where \( 0 < a < 1\).

  4. "Has steeper slopes and to left 2 units"

    • This would indicate: \[ g(x) = a |x + 2| \] where \( a > 1 \).

Conclusion

To summarize, from your descriptions, it sounds like you are identifying a variety of transformations on the parent function \( f(x) = |x| \). The transformations can include shifts horizontally (right or left) and changes in steepness (stretching or compressing).

If you need help more specific to a transformed function, please provide the exact transformations or equations you're considering!

You have to pick one of the choices that I sent I think it shifts to right 2 units but has less slopes

Based on your clarification that the transformed function shifts to the right by 2 units and has less steep slopes, the correct choice from your list would be:

"Less steep slope and shifted to right 2 units."

This corresponds well with the transformation of the parent function \( f(x) = |x| \) to a function that can be expressed as:

\[ g(x) = a |x - 2| \]

where \( 0 < a < 1 \) indicates the function is less steep, and the shift to the right is due to \( (x - 2) \).

If you have further questions or need more details, feel free to ask!