Sketch the graph of the polynomial function $$ p(x) = \cancel{\frac{1}{7}x}-2x -\cancel{x}+7 $$

Tap the blue points to see coordinates.

STEP 1:Find the x-intercepts

To find the x-intercepts solve, the equation $ \color{blue}{ \cancel{\frac{1}{7}x}-2x -\cancel{x}+7 = 0 } $

The solution of this equation is:

$$ \begin{matrix}x = \dfrac{ 49 }{ 20 } \end{matrix} $$

(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) = \cancel{\frac{1}{7}x}-2x -\cancel{x}+7 } $, so:

$$ \text{Y inercept} = p(0) = 7 $$

STEP 3:Find the end behavior

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

$$ \lim_{x \to -\infty} \left( \cancel{\frac{1}{7}x}-2x -\cancel{x}+7 \right) = \lim_{x \to -\infty} \frac{1}{7}x = \color{blue}{ -\infty } $$

The graph starts in the lower-left corner.

$$ \lim_{x \to \infty} \left( \cancel{\frac{1}{7}x}-2x -\cancel{x}+7 \right) = \lim_{x \to \infty} \frac{1}{7}x = \color{blue}{ \infty } $$

The graph ends in the upper-right corner.

Graphing Polynomials