Questions: QUESTION 4 Find the x-intercepts and y-intercept of the following function. f(x)=(x-1)(x+1)(x+2)

Solution Steps

To find the $x$-intercepts of the function, we need to determine the values of $x$ for which $f(x) = 0$. This involves solving the equation $(x-1)(x+1)(x+2) = 0$. The $y$-intercept is found by evaluating the function at $x = 0$, which gives $f(0)$.

To find the \(x\)-intercepts of the function \(f(x) = (x-1)(x+1)(x+2)\), we set the function equal to zero and solve for \(x\): \[ (x-1)(x+1)(x+2) = 0 \] The solutions to this equation are the values of \(x\) that make the function zero. Solving the equation, we find: \[ x = -2, \quad x = -1, \quad x = 1 \]

The \(y\)-intercept of the function is found by evaluating the function at \(x = 0\): \[ f(0) = (0-1)(0+1)(0+2) = (-1)(1)(2) = -2 \] Thus, the \(y\)-intercept is \(-2\).

Final Answer