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

Question

Determine which of the following functions $f (x) = c x, g (x) = c x^{2}, h (x) = c \sqrt{| x |}, and r (x) = \frac{c}{x}$ 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. $\begin{array}{cc} x & - 4 & - 1 & 0 & 1 & 4 \\ y & - 32 & - 2 & 0 & - 2 & - 32 \end{array}$

Answer 1

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 $g (x) = c x^{2}$ . The point $(- 4, - 32)$ is on the graph. So, substitute the point, $(- 4, - 32)$ , in $g (x) = c x^{2}$ .
$- 32 = c {(- 4)}^{2}$
$- 32 = c (16)$
$\frac{- 32}{16} = c$ Solving further, $c = - 2$ So, $g (x) = - 2 x^{2}$ Hence, the function that can be used to model the data is $g (x) = c x^{2}$ 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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