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

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.

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 \([-1.8889, -1.6667, 7, 25, 79]\).

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

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