Question

Graph$\left\{\left(-\mathbf{2},\mathbf{4}\right),\left(-\mathbf{1},\mathbf{1}\right),\left(\mathbf{0},\mathbf{0}\right),\left(\mathbf{1},\mathbf{1}\right),\left(\mathbf{2},\mathbf{4}\right)\right\}$. Determine whether the ordered pairs represent a linear function, a quadratic function, or an exponential function.

Short answer

The graph is given by:

The ordered pairs represent a quadratic function.

Step-by-step solution

Step 1. State the concept.

The equation of linear functions is given by $y=mx+b$. The quadratic equations and exponential functions are non-linear functions whose equations is given by$y=a{x}^2+bx+c$ and$y=a{b}^x$ respectively.

Step 2. Write an equation for the functions that models the data. 

Graph the points $\left\{\left(-\mathbf{2},\mathbf{4}\right),\left(-\mathbf{1},\mathbf{1}\right),\left(\mathbf{0},\mathbf{0}\right),\left(\mathbf{1},\mathbf{1}\right),\left(\mathbf{2},\mathbf{4}\right)\right\}$.

Step 3. State the interpretation of the graph.

From the graph, it can be observed that the ordered pairs represent a quadratic function.