# Determine the number of x-intercepts that appear on a graph of each function. f (x) = (x + 1)(x - 3)(x - 4) How many X-intercepts are there?

Feb 18, 2018

There are $3$ $x$-intercepts $\to \left(- 1 , 0\right) , \left(3 , 0\right) , \left(4 , 0\right)$

#### Explanation:

To find the $x$-intercepts, set the $y$ value or $f \left(x\right)$ equal to $0$.

$f \left(x\right) = 0$

$0 = \left(x + 1\right) \left(x - 3\right) \left(x - 4\right) \leftarrow$ Now set each term equal to $0$

• $\left(x + 1\right) = 0 \to x = - 1$
• $\left(x - 3\right) = 0 \to x = 3$
• $\left(x - 4\right) = 0 \to x = 4$

Since the $y$ value is $0$, with the above $x$ values, you can find the $x$-intercept points: $\left(- 1 , 0\right) , \left(3 , 0\right) , \left(4 , 0\right)$.