Algebra and Trigonometry 10th Edition

a) $g(x)=x^2-1$ b)$g(x)=-(x+1)^2+1$
a) We start with the graph of the function $f(x)=x^2$. Vertically shift $f(x)$ one unit downward to get the function from the given graph: $g(x)=x^2-1$ b) We start with the graph of the function $f(x)=x^2$. Reflect the graph of the function $f$ across the $x$-axis to get $a(x)=-x^2$. Then horizontally shift $a(x)$ one unit to the left to get $b(x)=-(x+1)^2$. Finally, vertically shift $b(x)$ one unit upward to get the function from the given graph: $g(x)=-(x+1)^2+1$