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4.2.3 Quiz: Parent Functions
Question 10 of 10
Which parent function is represented by the table?





x

y


-2
4


-1
1


0
0


1
1


2
4

44.22.33 Quiz: Parent Functions\newlineQuestion 1010 of 1010\newlineWhich parent function is represented by the table?\newline\begin{tabular}{|c|c|}\newline\hline x \boldsymbol{x} & y \boldsymbol{y} \\\newline\hline2-2 & 44 \\\newline\hline1-1 & 11 \\\newline\hline 00 & 00 \\\newline\hline 11 & 11 \\\newline\hline 22 & 44 \\\newline\hline\newline\end{tabular}

Full solution

Q. 44.22.33 Quiz: Parent Functions\newlineQuestion 1010 of 1010\newlineWhich parent function is represented by the table?\newline\begin{tabular}{|c|c|}\newline\hline x \boldsymbol{x} & y \boldsymbol{y} \\\newline\hline2-2 & 44 \\\newline\hline1-1 & 11 \\\newline\hline 00 & 00 \\\newline\hline 11 & 11 \\\newline\hline 22 & 44 \\\newline\hline\newline\end{tabular}
  1. Analyze pattern in table: Analyze the given table to identify the pattern between the xx and yy values.\newlineThe table shows the following pairs: (2,4)(-2, 4), (1,1)(-1, 1), (0,0)(0, 0), (1,1)(1, 1), and (2,4)(2, 4).\newlineWe need to determine the relationship between xx and yy that is consistent for all pairs.
  2. Identify relationship between xx and yy: Recognize that the yy values are the squares of the xx values for the pairs (2,4)(-2, 4), (1,1)(-1, 1), (1,1)(1, 1), and (2,4)(2, 4). The pair (0,0)(0, 0) also fits this pattern since 00 squared is 00.\newlineThis suggests that the parent function could be yy11, which is a quadratic function.
  3. Verify quadratic function: Verify the pattern for all given xx values by squaring each xx and checking if it equals the corresponding yy value.(2)2=4(-2)^2 = 4, (1)2=1(-1)^2 = 1, (0)2=0(0)^2 = 0, (1)2=1(1)^2 = 1, (2)2=4(2)^2 = 4. All the squared xx values match the yy values in the table.
  4. Conclude parent function: Conclude that the parent function represented by the table is the quadratic function y=x2y = x^2.

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