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Question

Write the equation for the given parent function and listed transformations.

1. x², right 1, reflect across the x-axis, vertical shrink by 1/3

2. √𝑥, reflect across the y-axis, vertical shrink by 1/3, up 1, horizontal shrink by 5/3

3. x³, left 2, down 1, horizontal stretch, by 3/4

4. |x|, vertical stretch by 2, horizontal shrink by 3, reflect across the y-axis.

Answer 1

1. -1/3(x-1)² : negatives outside the parentheses will reflect over the x-axis, coefficients between 0-1 outside parentheses cause vertical shrinks (greater than 1 cause stretch), subtracting inside the parentheses will move things right (adding will move left)
2. 1/3(√-5/3x)+1 : negatives in the parentheses (or root) causes reflections over y, coefficients greater than 1 in root will causes horizontal shrinks (between 0-1 causes stretches), adding outside the root shifts up (subtracting shifts down)
3. (3/4x+3)³-1
4. 2|-3x|

The rules for transformations are generally thought of as: if it happens outside the parentheses/root/bracket the change that happens is vertical and it changes how you would logically expect it to, when it's inside though, the change is horizontal and it happens in the "reverse" of what you'd immediately assume