Chapter 5 Polynomial and Rational Functions

Chapter 5 Using Technology

Using Desmos to graph Quadratic, Polynomial, and Rational Equations

In Section 5.1, the quadratic functions can be graphed with this Desmos Graphing parabola tool.

Example from 5.3 Graphing Polynomial Equations

Finding the x-Intercepts of a Polynomial Function by Factoring

We can use technology to find the intercepts of[latex]\,f\left(x\right)={x}^{3}-5{x}^{2}-x+5[/latex] by graphing instead of by factoring.

Show Solution

Type the equation into Desmos. Then click on each of the x-intercepts to see it's coordinates.

Polynomial graph intersects the x-axis at x= -1, 1, and 5.
This Desmos matches the graph in Figure 4.
Graph of f(x)=x^3-5x^2-x+5 with its three intercepts (-1, 0), (1, 0), and (5, 0).
Figure 4.

There are three x-intercepts:[latex]\,\left(-1,0\right),\left(1,0\right),\,[/latex]and[latex]\,\left(5,0\right).\,[/latex]See Figure 4.

Back to Section 5.3.

Example from 5.6 Graphing Rational Equations

Graphing a Rational Function

Sketch a graph of[latex]\,f\left(x\right)=\frac{\left(x+2\right)\left(x-3\right)}{{\left(x+1\right)}^{2}\left(x-2\right)}.[/latex]

Show Solution

Type the equation into Desmos. Click on a critical point to see it's coordinates. The graph makes it easy to visualize the vertical asymptotes.

Graph of a Rational function with zeroes at x=-2 and 3.The Desmos graph matches the graph in Figure 21.

 

Graph of f(x)=(x+2)(x-3)/(x+1)^2(x-2)
Figure 21. Vertical asymptotes at x=-1 and x=2, its horizontal asymptote at y=0, and its intercepts at (-2, 0), (0, 3), and (3, 0)

Back to Section 5.6.

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