# Determine which of the following functionsf(x)=cx, g(x)=cx^{2}, h(x)=csqrt{|x|}, text{and} r(x)= frac{c}{x}

Determine which of the following functions can be used to model the data and determine the value of the constant c that will make the function fit the data in the table. $\begin{array}{|cccccc|}\hline x& -4& -1& 0& 1& 4\\ y& -32& -2& 0& -2& -32\\ \hline\end{array}$

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Consider the given function and the table. Now, with the help of the values given in the table, plot a graph as, Here, it can be seen that by plotting the data, the obtained graph represents a parabola. Therefore, the function which represents the data table is $g\left(x\right)=c{x}^{2}$. The point is on the graph. So, substitute the point, , in $g\left(x\right)=c{x}^{2}$.
$-32=c{\left(-4\right)}^{2}$
$-32=c\left(16\right)$
$\frac{-32}{16}=c$ Solving further, So, Hence, the function that can be used to model the data is $g\left(x\right)=c{x}^{2}$ and the value of constant is .