methods 3

first find the range of f(x) by competing the square, then use that range(output) of the inner function as the input of the outer function. do g(-4)

dilation parallel to the x-axis affects the x-value. dilation parallel to the y axis affects the y value. also remember to take out the dilation factor out the brackets before doing the translation!

first, obvious one, 9/4 units up. then its dilate by factor A parallel to the x-axis and translated by factor B left/right. so do two simultaneous equations and find a and B. dont flip the dilation for A because it is simply implied.

when they mention, width, think about margin of error. Here they mention the new interval has a greater width, hence has a greater margin of error than the origiinal. Hence, put togehter the inequality and solve it.

g(x)=sin(2x)

add to bound refernce