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Is this function linear, quadratic, or exponential?





x

y


-3
0.1


-2
0.3


-1
0.9


0
2.7


1
8.1

Is this function linear, quadratic, or exponential?\newline\begin{tabular}{|c|c|}\newline\hlinex x & y y \\\newline\hline3-3 & 00.11 \\\newline\hline2-2 & 00.33 \\\newline\hline1-1 & 00.99 \\\newline\hline 00 & 22.77 \\\newline\hline 11 & 88.11 \\\newline\hline\newline\end{tabular}

Full solution

Q. Is this function linear, quadratic, or exponential?\newline\begin{tabular}{|c|c|}\newline\hlinex x & y y \\\newline\hline3-3 & 00.11 \\\newline\hline2-2 & 00.33 \\\newline\hline1-1 & 00.99 \\\newline\hline 00 & 22.77 \\\newline\hline 11 & 88.11 \\\newline\hline\newline\end{tabular}
  1. Check y-value changes: Check if the y-values change at a constant rate as xx increases by 11. Calculate the differences between consecutive y-values.\newline0.30.1=0.20.3 - 0.1 = 0.2\newline0.90.3=0.60.9 - 0.3 = 0.6\newline2.70.9=1.82.7 - 0.9 = 1.8\newline8.12.7=5.48.1 - 2.7 = 5.4
  2. Not linear function: Notice that the differences are not constant, so the function is not linear.
  3. Check y-value ratios: Check if the ratios of consecutive y-values are constant to see if the function is exponential. Calculate the ratios.\newline0.30.1=3\frac{0.3}{0.1} = 3\newline0.90.3=3\frac{0.9}{0.3} = 3\newline2.70.9=3\frac{2.7}{0.9} = 3\newline8.12.7=3\frac{8.1}{2.7} = 3
  4. Exponential function: Since the ratios of consecutive yy-values are constant, the function is exponential.

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