Find the \( x \)-intercepts and \( y \)-intercept of the following function. \[ f(x)=(x-4)(x+1)(x+8) \]

To find the \( x \)-intercepts of the function \( f(x)=(x-4)(x+1)(x+8) \), set \( f(x) = 0 \). This gives us: \[ (x-4)(x+1)(x+8) = 0 \] The \( x \)-intercepts occur when any of the factors equal zero: 1. \( x - 4 = 0 \) → \( x = 4 \) 2. \( x + 1 = 0 \) → \( x = -1 \) 3. \( x + 8 = 0 \) → \( x = -8 \) Thus, the \( x \)-intercepts are \( (4, 0) \), \( (-1, 0) \), and \( (-8, 0) \). To find the \( y \)-intercept, evaluate \( f(0) \): \[ f(0) = (0-4)(0+1)(0+8) = (-4)(1)(8) = -32 \] So, the \( y \)-intercept is \( (0, -32) \). In summary, the intercepts are: - \( x \)-intercepts: \( (4, 0) \), \( (-1, 0) \), \( (-8, 0) \) - \( y \)-intercept: \( (0, -32) \)