Question

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|} \h

Transformations of functions
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asked 2021-06-08

Tabular representations for the functions f, g, and h are given below. Write g(x) and h(x) as transformations of f(x). \(\begin{array}{|c|c|c|c|c|c|} \\ x & -2 & -1 & 0 & 1 & 2 \\ \\ f(x) & -2 & -1 & -3 & 1 & 2 \\ \end{array}\)

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

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

Answers (1)

2021-06-09
Since we add 1 to the values of x for the function f to get the values of x for the function g(x).
And the values of y are the same in both function. Therefore, The function g(x) is a horizontal shift of f(x).
The function g(x) is shifted 1 unit to the right.
Since we add 1 to the values of y for the function f to get the values of y for the function h(x).
And the values of x are the same in both function. Therefore, The function h(x) is a vertical shift of f(x).
The function h(x) is shifted 1 unit up.
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