Answer:
- Horizontal reflection
- Shift up
- Shift right
- Vertical stretch
Explanation:
The transformations we typically study are ...
g(x) = -f(x) . . . vertical reflection
g(x) = f(x) +h . . . vertical shift up by h
g(x) = k·f(x) . . . vertical expansion by a factor of k
g(x) = f(-x) . . . horizontal reflection
g(x) = f(x -h) . . . right shift by h
g(x) = f(k·x) . . . horizontal compression by a factor of k
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You have g(x)=3f(-(x-2)) +1.
The external factor of 3 is a vertical stretch.
The minus sign multiplying the argument of f(x) is a horizontal reflection.*
The -2 in parentheses is a right shift of 2.
The +1 added to the function value is a shift up by 1.
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* The parent function is symmetrical about the y-axis, so a horizontal reflection does not change the graph in any way. It may as well be ignored. However, the sign shows up in the transformation, so we have listed it--even though you cannot detect it in the graph.
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In the attached, f(x) is shown as a blue dashed line.