Chapter 11, Problem 1RVS

To determine

The graph for the function, $f\left(x\right)=3x^2$ and match the correct graph from the set of options as provided.

Answer to Problem 1RVS

Solution:

The correct match for the function is the graph in the option B.

Explanation of Solution

Given Information:

The function, $f\left(x\right)=3x^2$

The set of options for correct solution is,

Determine the values of the function, $f\left(x\right)=3x^2$ for some random values of x as,

Put, $x=0$

$\begin{array}{c}f\left(x\right)=3{\left(0\right)}^2\\ =0\end{array}$

Put, $x=1$

$\begin{array}{c}f\left(x\right)=3{\left(1\right)}^2\\ =3\end{array}$

Put, $x=-1$

$\begin{array}{c}f\left(x\right)=3{\left(-1\right)}^2\\ =3\end{array}$

Put, $x=2$

$\begin{array}{c}f\left(x\right)=3{\left(2\right)}^2\\ =12\end{array}$

Put, $x=-2$

$\begin{array}{c}f\left(x\right)=3{\left(-2\right)}^2\\ =12\end{array}$

The point table to plot the graph is as follow,

$\begin{array}{cc}x& f\left(x\right)=3x^2\\ 0& 0\\ 1& 3\\ -1& 3\\ 2& 12\\ -2& 12\end{array}$

Thus, coordinates are $\left(0,0\right),\left(1,3\right),\left(-1,3\right),\left(2,12\right),\left(-2,12\right)$.

Observe that obtained coordinates matches the graph in option B with intercept at point $\left(0,0\right)$.

Hence, the correct match for the function is the graph in the option B.