Determine which of the following functions f(x)=cx, g(x)=cx2, h(x)=c|x|, and r(x)= cx 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. x−4−1014y−32−20−2−32

Question

Determine which of the following functions f(x)=cx, g(x)=cx2, h(x)=c|x|, and r(x)= cx 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. x−4−1014y−32−20−2−32

Sadie Eaton · Accepted Answer

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(x)=cx2. The point (−4, −32) is on the graph. So, substitute the point, (−4, −32), in g(x)=cx2. −32=c(−4)2 −32=c(16) −3216=c Solving further, c= −2 So, g(x)= −2x2 Hence, the function that can be used to model the data is g(x)=cx2 and the value of constant is c= −2.

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

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