Question

Match the function with its graph.

1. $f\left(x\right)=x^2$
2. $f\left(x\right)=x^3$
3. $f\left(x\right)=\sqrt{x}$
4. $f\left(x\right)=\left|x\right|$
   

Short answer

The functions can be matched with graph as

$\begin{array}{l}\mathrm{{\rm I}}\leftrightarrow c\\ \mathrm{{\rm I}{\rm I}}\leftrightarrow b\\ \mathrm{{\rm I}{\rm I}{\rm I}}\leftrightarrow d\\ \mathrm{Ⅳ}\leftrightarrow a\end{array}$

Step-by-step solution

Step 1. Use definition of a graph of a function.

The graph of a function f is the set of all points in the plane of the form (x, f(x)).

Step 2. Match the graph with the function.

We are given the following 4 functions

$\begin{array}{l}\left(a\right)f\left(x\right)=x^2\\ \left(b\right)f\left(x\right)=x^3\\ \left(c\right)f\left(x\right)=\sqrt{x}\\ \left(d\right)f\left(x\right)=\left|x\right|\end{array}$

We are also given the following 4 graphs

Observe that: $\left(a\right)f\left(x\right)=x^2$has domain of all real numbers and range of only positive numbers and zero. Also graph is a parabola. Clearly only graph (Ⅳ) fits this criterion.

Observe that: $\left(b\right)f\left(x\right)=x^3$has domain of all real numbers and range is also all real numbers. Clearly only graph (Ⅱ) fits this criterion.

Observe that: $\left(c\right)f\left(x\right)=\sqrt{x}$has domain of all positive numbers and range of all positive numbers. Clearly only graph (Ⅰ) fits this criterion.

Observe that: $\left(d\right)f\left(x\right)=\left|x\right|$has domain of all real numbers and range of only positive numbers and zero. Graph is also symmetric about y axis as $\left|x\right|=\left|-x\right|$.Clearly only graph (Ⅲ) fits this criterion.

Step 3. Evaluate the results.

The correct matching is as shown below: