precal question

Question

A function f is given, and the indicated transformations are applied to its graph (in the given order). Write the equation for the final transformed graph.

f(x) = x²; shift 7 units to the left and reflect in the x-axis

Answer 1

Starting with y=x², move it left by ADDING 7 to x. (To move x values, we always use the sign opposite the direction that we want to move, so + for left or - for right.) We also put it in parentheses so the whole thing is squared: y=(x+7)².

To reflect over the y-axis, we want to change the signs of the x values, so we put a negative in front of x: y=(-x+7)².

Hope this helps!

Let me know if you have any questions, and have fun mathing!