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

QUESTION 4

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

Transcript text: QUESTION 4 Find the $x$-intercepts and $y$-intercept of the following function. \[ f(x)=(x-1)(x+1)(x+2) \]

Solution

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 $f(0)$.

Step 1: Find the \(x\)-intercepts

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: \[ x = -2, \quad x = -1, \quad x = 1 \]

Step 2: Find the \(y\)-intercept

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

\(\boxed{x = -2, \, x = -1, \, x = 1, \, y = -2}\)

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