onal Functions
Part 1 of 3
The graphs of two polynomials $p$ and $d$ are shown in the accompanying figure. Answer each of the following for the rational function $f=\frac{p}{d}$ :
a. Find the domain of $f$.
b. Find the $x$-intercept(s) of $f$.
c. Sketch the graph of $f$.
a. The domain of $f$ is
(Type your answer in interval notation.)
\(\boxed{\text{Final Answer: Without the explicit functions for } p \text{ and } d \text{ or the accompanying figure, we cannot provide a specific answer. However, the general process to find the domain of a rational function is to set the denominator equal to zero and solve for } x. \text{ The domain of the function is all real numbers except the solutions to this equation.}}\)
Step 1 :The domain of a rational function is all real numbers except where the denominator is zero. In this case, the denominator is the function \(d\). We need to find the x-values where \(d\) is zero. However, without the accompanying figure or the explicit functions for \(p\) and \(d\), it's impossible to provide a specific answer.
Step 2 :If we had the explicit functions for \(p\) and \(d\), we could set \(d\) equal to zero and solve for \(x\) to find the values that are not in the domain of \(f\).
Step 3 :For example, if \(d(x) = x^2 - 4\), we would set this equal to zero and solve for \(x\):
Step 4 :The output would be \([-2, 2]\), meaning that the domain of \(f\) is all real numbers except -2 and 2. In interval notation, this would be \((-\infty, -2) \cup (-2, 2) \cup (2, \infty)\).
Step 5 :\(\boxed{\text{Final Answer: Without the explicit functions for } p \text{ and } d \text{ or the accompanying figure, we cannot provide a specific answer. However, the general process to find the domain of a rational function is to set the denominator equal to zero and solve for } x. \text{ The domain of the function is all real numbers except the solutions to this equation.}}\)