Questions: Find the x - and y-intercepts for the function. f(x) = (x+6)/(x^2+4) Enter your answers as points, (a, b). The x-intercept is The y-intercept is

Solution Steps

To find the $x$-intercept, we need to set $f(x) = 0$ and solve for $x$. For the $y$-intercept, we need to evaluate $f(0)$.

1. To find the $x$-intercept, set the numerator of the function equal to zero and solve for $x$.
2. To find the $y$-intercept, substitute $x = 0$ into the function and solve for $f(0)$.

To find the \( x \)-intercept, we set the function \( f(x) \) equal to zero: \[ f(x) = 0 \implies \frac{x + 6}{x^2 + 4} = 0 \] This occurs when the numerator is zero: \[ x + 6 = 0 \implies x = -6 \] Thus, the \( x \)-intercept is the point: \[ (-6, 0) \]

To find the \( y \)-intercept, we evaluate the function at \( x = 0 \): \[ f(0) = \frac{0 + 6}{0^2 + 4} = \frac{6}{4} = \frac{3}{2} \] Thus, the \( y \)-intercept is the point: \[ (0, \frac{3}{2}) \]

Final Answer