Finding the x and y Intercepts of Any Function

[Jason]

Finding the x and y intercepts is as simple as plugging 0 into the "other" variable.

But x or y variables to plug-in must be in the numerator.

ex. a

What are the x intercepts?

\(y = \dfrac{4x + 3}{2x - 3}\)

\(0 = \dfrac{4x + 3}{2x - 3} \)

\((2x - 3) 0 = \dfrac{4x - 3}{2x - 3}(2x - 3)\)

\(0 = \dfrac{(4x + 3)}{1}\)


\(0 = 4x + 3 \)

\(0 - 3 = 4x + 3 - 3\)

\(-3 = 4x\)

\(-\dfrac{3}{4} = \dfrac{4x}{4}\)

\(-\dfrac{3}{4} = x\)

x intercept is \((-\dfrac{3}{4}, 0)\).

ex. a

What are the y intercepts?

\(y = 5x^{2} - x + 5\)

\(y = 5(0)^{2} - (0) + 5\)

\(y = 5\)

y intercept is \((0, 5)\).