Find the function that is finally graphed after the following transformations are applied to the graph of y=x

Question

Find the function that is finally graphed after the following transformations are applied to the graph of

y=x

in the order listed.

​(1)  Reflect about the x-axis

​(2)  Shift down 6 units

​(3)  Shift left 5 units

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Part 1

y=enter your response here

Answer 1

f=f(x) reflected over the x axis is y = -f(x)

y = x reflected over x axis is y = - x

Shift down by 6 means subtract 6 outside of what's happening to x: y = -x - 6

Shift left by 5 means add 5 inside what's happening to x: y = -(x+5) - 6

Distribute: y = - x - 5 - 6

y = - x - 11