Tabular representations for the functions f, g, and h are given below. Write g(x) and h(x) as transformations of f (x)

Tabular representations for the functions f, g, and h are given below. Write g(x) and h(x) as transformations of f (x).

$$\begin{array}{|c|c|c|c|c|c|} \hline x & -2 & -1 & 0 & 1 & 2 \\ \hline f(x) & -1 & -3 & 4 & 2 & 1 \\ \hline \end{array}$$

$$\begin{array}{|c|c|c|c|c|c|} \hline x & -3 & -2 & -1 & 0 & 1 \\ \hline g(x) & -1 & -3 & 4 & 2 & 1 \\ \hline \end{array}$$

$$\begin{array}{|c|c|c|c|c|c|} \hline x & -2 & -1 & 0 & 1 & 2 \\ \hline h(x) & -2 & -4 & 3 & 1 & 0 \\ \hline \end{array}$$

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Usamah Prosser
Since we subtract 1 from the values of x for the function f to get the values of x for the function g(r).
And the values of y are the same in both function.
Therefore, The function g(z) is « horizontal shift of f(z).
The function g(z) is shifted 1 unit to the left.
Since we subtract 1 from the values of y for the function f to get the values of y for the function A(z).
And the values of x are the same in both function. Therefore, The function A(z) is a vertical shift of f(x).
The function f(x) is shifted 1 unit down.