Q. Is this function linear, quadratic, or exponential?\begin{tabular}{|c|c|}\hlinex & y \\\hline−3 & 0.1 \\\hline−2 & 0.3 \\\hline−1 & 0.9 \\\hline 0 & 2.7 \\\hline 1 & 8.1 \\\hline\end{tabular}
Check y-value changes: Check if the y-values change at a constant rate as x increases by 1. Calculate the differences between consecutive y-values.0.3−0.1=0.20.9−0.3=0.62.7−0.9=1.88.1−2.7=5.4
Not linear function: Notice that the differences are not constant, so the function is not linear.
Check y-value ratios: Check if the ratios of consecutive y-values are constant to see if the function is exponential. Calculate the ratios.0.10.3=30.30.9=30.92.7=32.78.1=3
Exponential function: Since the ratios of consecutive y-values are constant, the function is exponential.
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