Questions: Algebra II Sem 2 Apex Learning 3.11.3 Quiz: Comparing and Analyzing Function Types Question 1 of 10 The function g(x) is a transformation of the parent function f(x). Decide how f(x) was transformed to make g(x). f(x) x y -2 1/9 -1 1/3 2 9 3 27 4 81 g(x) x y -2 -17/9 -1 -5/3 2 7 3 25 4 79 A. Reflection across the line y=x B. Horizontal or vertical reflection C. Horizontal or vertical stretch D. Horizontal or vertical shift

Algebra II Sem 2 Apex Learning 3.11.3 Quiz: Comparing and Analyzing Function Types Question 1 of 10 The function g(x) is a transformation of the parent function f(x). Decide how f(x) was transformed to make g(x). f(x) x y -2 1/9 -1 1/3 2 9 3 27 4 81 g(x) x y -2 -17/9 -1 -5/3 2 7 3 25 4 79 A. Reflection across the line y=x B. Horizontal or vertical reflection C. Horizontal or vertical stretch D. Horizontal or vertical shift
Transcript text: Algebra II Sem 2 Apex Learning 3.11.3 Quiz: Comparing and Analyzing Function Types Question 1 of 10 The function $g(x)$ is a transformation of the parent function $f(x)$. Decide how $f(x)$ was transformed to make $g(x)$. \begin{tabular}{|c|c|} \hline \multicolumn{2}{|c|}{$\boldsymbol{f}(\boldsymbol{x})$} \\ \hline $\boldsymbol{x}$ & $\boldsymbol{y}$ \\ \hline-2 & $\frac{1}{9}$ \\ \hline-1 & $\frac{1}{3}$ \\ \hline 2 & 9 \\ \hline 3 & 27 \\ \hline 4 & 81 \\ \hline \end{tabular} \begin{tabular}{|c|c|} \hline \multicolumn{2}{|c}{$\boldsymbol{g ( x )}$} \\ \hline $\boldsymbol{x}$ & $\boldsymbol{y}$ \\ \hline-2 & $-\frac{17}{9}$ \\ \hline-1 & $-\frac{5}{3}$ \\ \hline 2 & 7 \\ \hline 3 & 25 \\ \hline 4 & 79 \\ \hline \end{tabular} A. Reflection across the line $y=x$ B. Horizontal or vertical reflection C. Horizontal or vertical stretch D. Horizontal or vertical shift
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Solution

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Solution Steps

To determine how the function \( f(x) \) was transformed to become \( g(x) \), we need to analyze the changes in the \( y \)-values for corresponding \( x \)-values. By comparing the differences between the \( y \)-values of \( f(x) \) and \( g(x) \), we can identify if there is a consistent shift, reflection, or stretch. In this case, it appears that there is a consistent vertical shift between the two functions.

Step 1: Analyze the Transformation

To determine the transformation from \( f(x) \) to \( g(x) \), we compare the \( y \)-values of both functions for the same \( x \)-values. The \( y \)-values for \( f(x) \) are \([0.1111, 0.3333, 9, 27, 81]\) and for \( g(x) \) are \([-1.8889, -1.6667, 7, 25, 79]\).

Step 2: Calculate the Differences

We calculate the differences between the corresponding \( y \)-values of \( f(x) \) and \( g(x) \): \[ \begin{align_} -1.8889 - 0.1111 &= -2.0000, \\ -1.6667 - 0.3333 &= -2.0000, \\ 7 - 9 &= -2, \\ 25 - 27 &= -2, \\ 79 - 81 &= -2. \end{align_} \]

Step 3: Identify the Transformation

The differences between the \( y \)-values are consistent and equal to \(-2\). This indicates a vertical shift of \( f(x) \) downward by 2 units to obtain \( g(x) \).

Final Answer

\(\boxed{\text{D. Horizontal or vertical shift}}\)

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