For each table, identify the parent function that corresponds to the new function given. Then graph by hand both the parent function and new function on the grids provided. Finally, identify any reflections, shifts, stretches, shrinks, even or odd or neither behavior. Be specific about the shifts (be sure to include the term vertical or horizontal when applicable). If the graph does not contain one of these changes, write none in the box provided. Parent function New function: g(x) =|-(x-2)| f(x) = Reflections: Shifts (Vertical / Horizontal): Stretches / Shrinks: Even, Odd, or Neither: Parent function New function: g(x) = x2 - 6 f(x) = Reflections: Shifts (Vertical / Horizontal): Stretches / Shrinks: Even, Odd, or Neither: Parent function New function: g(x) = |x + 3| + 1 f(x) = Reflections: Shifts (Vertical / Horizontal): Stretches / Shrinks: Even, Odd, or Neither:
For each table, identify the parent function that corresponds to the new function given. Then graph by hand both the parent function and new function on the grids provided. Finally, identify any reflections, shifts, stretches, shrinks, even or odd or neither behavior. Be specific about the shifts (be sure to include the term vertical or horizontal when applicable). If the graph does not contain one of these changes, write none in the box provided.
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Parent function |
New function: g(x) =|-(x-2)| |
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f(x) = |
Reflections: |
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Shifts (Vertical / Horizontal): |
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Stretches / Shrinks: |
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Even, Odd, or Neither: |
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Parent function |
New function: g(x) = x2 - 6 |
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f(x) = |
Reflections: |
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Shifts (Vertical / Horizontal): |
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Stretches / Shrinks: |
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Even, Odd, or Neither: |
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Parent function |
New function: g(x) = |x + 3| + 1 |
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f(x) = |
Reflections: |
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Shifts (Vertical / Horizontal): |
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Stretches / Shrinks: |
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Even, Odd, or Neither: |
New Function: .
Parent Function: .
Reflections: The new function is obtained by replacing by . So, there will be reflection along y-axis. However, the parent function is symmetrical along y-axis.
Shifts(Vertical/ Horizontal): There is no number added or subtracted to the function, so, there will be no vertical shift. Since, 2 is subtracted from , so, there will be a horizontal shift to the right by 2 units.
Stretches/ Shrinks: Since, the coefficient of is in the new function, so, there will be no stretching, or, shrinking.
Even, Odd, or, neither: Here, , so, it is neither even nor odd function.
The graph is as follows:
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