Question

Which transformations take f(x)=3x+1 to g(x)=−3x-5 ?

Answer 1

reflection over the x-axis and a translation 4 units down Refelcting f(x) over the x axis gives -f(x)=-3x-1 Subtracting a constant from -f(x) moves the graph of -f(x) that many units down. -f(x)-4=-3x-5=g(x) This shows that g(x) is obtained by reflecting f(x) over the x-axis and then translating 4 units down.