Polynomial graphing calculator

This page helps you explore polynomials with degrees up to 4. The roots (x-intercepts), signs, local maxima and minima, increasing and decreasing intervals, points of inflection, and concave up-and-down intervals can all be calculated and graphed.

problem

Sketch the graph of the polynomial function

$$ p(x) = 3x $$

solution

Tap the blue points to see their coordinates.

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explanation

STEP 1:Find the x-intercepts

To find the x-intercepts solve, the equation $ \color{blue}{ 3x = 0 } $

The solution of this equation is:

\begin{matrix}x = 0 \end{matrix}

(you can use the step-by-step polynomial equation solver to see a detailed explanation of how to solve the equation)

STEP 2:Find the y-intercepts

To find the y-intercepts, substitute $ x = 0 $ into $ \color{blue}{ p(x) = 3x } $, so:

$$ \text{Y inercept} = p(0) = 0 $$

STEP 3:Find the end behavior

The end behavior of a polynomial is the same as the end behavior of a leading term.

$$ \lim_{x \to -\infty} \left( 3x \right) = \lim_{x \to -\infty} 3x = \color{blue}{ -\infty } $$

The graph starts in the lower-left corner.

$$ \lim_{x \to \infty} \left( 3x \right) = \lim_{x \to \infty} 3x = \color{blue}{ \infty } $$

The graph ends in the upper-right corner.

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Script name : polynomial-graphing-calculator

Form values: 3x , g , Sketch the graph of polynomial 3x - mathportal

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Polynomial Graphing Calculator
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