Question

Please help! Functions and Relations. The function h(x) is a transformation of the square root function, f(x)= square root of x. What function is h(x)? Thanks!

Answer 1

In general, given a function g(x), a horizontal shift is given by the transformation below

`\begin{gathered} g(x)\rightarrow g(x-a) \\ a>0\rightarrow\text{ a units to the right} \\ a<0\rightarrow\text{ a units to the left} \end{gathered}`

Thus, in our case, notice that the graph of h(x) is that of f(x) shifted 1 unit to the left; then,

`h(x)=√(x+1)`

The answer is option C.