Question

Use the tables to answer the question.

x
f(x)
−1
0
0 1
1 2
2 9


x
g(x)
3 0
4 1
5 2
6 9
If y=f(x)
is the original function and y=g(x)
the horizontally translated function, by how many k units is the original function translated?



(1 point)
The original function has been translated by
units.

Answer 1

To determine the horizontal translation of the function \(y = f(x)\) into \(y = g(x)\), we need to compare the corresponding outputs of the two functions.

The values given in the tables for \(f(x)\) are:

\[
\begin{align*}
f(-1) &= 0 \\
f(0) &= 1 \\
f(1) &= 2 \\
f(2) &= 9 \\
\end{align*}
\]

The values given in the tables for \(g(x)\) are:

\[
\begin{align*}
g(3) &= 0 \\
g(4) &= 1 \\
g(5) &= 2 \\
g(6) &= 9 \\
\end{align*}
\]

Now, let's analyze the outputs of both functions:

- For \(f(-1) = 0\) and \(g(3) = 0\): This indicates a shift to the right by 4 units because \(-1 + 4 = 3\).
- For \(f(0) = 1\) and \(g(4) = 1\): This also confirms a shift to the right by 4 units because \(0 + 4 = 4\).
- For \(f(1) = 2\) and \(g(5) = 2\): This confirms a shift to the right by 4 units since \(1 + 4 = 5\).
- For \(f(2) = 9\) and \(g(6) = 9\): This again confirms a shift to the right by 4 units because \(2 + 4 = 6\).

In all comparisons, each \(x\) value in \(f(x)\) translates to an \(x\) value in \(g(x)\) that is 4 units greater, indicating a horizontal translation to the right.

Thus, the original function \(y = f(x)\) has been translated by **4 units** to form the function \(y = g(x)\).

The original function has been translated by **4** units.