Determine which of the following functions f(x)=cx, g(x)=cx^{2}, h(x)=csqrt{|x|}, text{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}{|c|c|} hline x & -4 & -1 & 0 & 1 & 4 hline y & -32 & -2 & 0 & -2 & -32 hline end {array}

Question
Modeling data distributions
asked 2021-02-02
Determine which of the following functions \(\displaystyle{f{{\left({x}\right)}}}={c}{x},\ {g{{\left({x}\right)}}}={c}{x}^{{{2}}},\ {h}{\left({x}\right)}={c}\sqrt{{{\left|{x}\right|}}},\ \text{and}\ {r}{\left({x}\right)}=\ {\frac{{{c}}}{{{x}}}}\) 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. \(\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left|{c}\right|}{c}{\mid}\right\rbrace}{h}{l}\in{e}{x}&-{4}&-{1}&{0}&{1}&{4}\backslash{h}{l}\in{e}{y}&-{32}&-{2}&{0}&-{2}&-{32}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}\)

Answers (1)

2021-02-03
Consider the given function and the table. Now, with the help of the values given in the table, plot a graph as, image 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 \(\displaystyle{g{{\left({x}\right)}}}={c}{x}^{{{2}}}\). The point \(\displaystyle{\left(-{4},\ -{32}\right)}\) is on the graph. So, substitute the point, \(\displaystyle{\left(-{4},\ -{32}\right)}\), in \(\displaystyle{g{{\left({x}\right)}}}={c}{x}^{{{2}}}\).
\(\displaystyle-{32}={c}{\left(-{4}\right)}^{{{2}}}\)
\(\displaystyle-{32}={c}{\left({16}\right)}\)
\(\displaystyle{\frac{{-{32}}}{{{16}}}}={c}\) Solving further, \(\displaystyle{c}=\ -{2}\) So, \(\displaystyle{g{{\left({x}\right)}}}=\ -{2}{x}^{{{2}}}\) Hence, the function that can be used to model the data is \(\displaystyle{g{{\left({x}\right)}}}={c}{x}^{{{2}}}\) and the value of constant is \(\displaystyle{c}=\ -{2}\).
0

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