What are the asymptotes for y = - 4 x + 2 and how do you graph the function?

Question

What are the asymptotes for       y    =    -          4              x        +        2             and how do you graph the function?

graulhavav9 · Accepted Answer

The asymptotes are at x=−2 and y0, this is because when x=−2 the denominator would equal 0 which cannot be solved. The y=0 asymptote is caused because as

x \to \infty

, the number will get so small and close to 0, but never reach 0.

The graph is that of

y = \frac{1}{x}

but shifted to the left by 2, and flipped in the x-axis. The curves will be more rounded as the numerator is a larger number.

Graph of

y = \frac{1}{x}

graph{1/x [-10, 10, -5, 5]}

Graph of

y = \frac{4}{x}

graph{4/x [-10, 10, -5, 5]}

Graph of

y = - \frac{4}{x}

graph{-4/x [-10, 10, -5, 5]}

Graph of

y = - \frac{4}{x + 2}

graph{-4/(x+2) [-10, 10, -5, 5]}

What are the asymptotes for y=−4/x+2 and how do you graph the function?

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Answer & Explanation

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