Sketch the graph of the polynomial function $$ p() = -\cancel{6}+ \cancel{6}-4+ \cancel{1} -\cancel{1}+ \cancel{2} -\cancel{2}+ \cancel{3} -\cancel{3} $$
Tap the blue points to see coordinates.
STEP 1:Find the x-intercepts
To find the x-intercepts solve, the equation $ \color{blue}{ -\cancel{6}+ \cancel{6}-4+ \cancel{1} -\cancel{1}+ \cancel{2} -\cancel{2}+ \cancel{3} -\cancel{3} = 0 } $
Since above equation has no solutions we conclude that
polynomial has no x-intecepts.
(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 $ = 0 $ into $ \color{blue}{ p() = -\cancel{6}+ \cancel{6}-4+ \cancel{1} -\cancel{1}+ \cancel{2} -\cancel{2}+ \cancel{3} -\cancel{3} } $, so:
$$ \text{Y inercept} = p(0) = -4 $$STEP 3:Find the end behavior
The end behavior of a polynomial is the same as the end behavior of a leading term.
$$ \lim_{x \to -\infty} \left( -\cancel{6}+ \cancel{6}-4+ \cancel{1} -\cancel{1}+ \cancel{2} -\cancel{2}+ \cancel{3} -\cancel{3} \right) = \lim_{x \to -\infty} -6 = \color{blue}{ -\infty } $$The graph starts in the lower-left corner.
$$ \lim_{x \to \infty} \left( -\cancel{6}+ \cancel{6}-4+ \cancel{1} -\cancel{1}+ \cancel{2} -\cancel{2}+ \cancel{3} -\cancel{3} \right) = \lim_{x \to \infty} -6 = \color{blue}{ -\infty } $$The graph ends in the lower-right corner.