Solving for a Variable
Let $f(x, y)=2^{x}+9 x y$, find $f(0,-3), f(-3,2)$, and $f(3,2)$.
$f(0,-3)=\square$ (Simplify your answer.)
$f(-3,2)=\square$ (Simplify your answer.)
$f(3,2)=\square$ (Simplify your answer.)
Polynomial Division
Find the remainder when the polynomial \( f(x) = 3x^4 - 2x^3 + 4x^2 - 5x + 1 \) is divided by the polynomial \( g(x) = x^2 - 3x + 2 \).
Synthetic Division
Given the function \(f(x) = x^4 - 3x^3 + 2x^2 - x - 1\). Find the derivative of the function using synthetic division and algebraic concepts.
Dividing
Let \( f(x) = 3x^2 + 5x - 2 \). Find \( f'(2) \) and then divide it by 2.
Finding the Domain
Find the domain of the function \(f(x) = \frac{1}{\sqrt{x^2 - 9}}\)
Finding the Range
Find the range of the function \( f(x) = x^2 + 5x + 6 \).
Finding the Domain and Range
Find the domain and range of the function \( f(x) = \sqrt{x^2 - 9} \)
Finding the Asymptotes
Find the vertical and horizontal asymptotes of the function \(f(x) = \frac{x^2 - 4}{x - 2}\).
Quadratic Inequalities
Solve the quadratic inequality \(x^2 - 3x - 4 > 0\)
Rational Inequalities
Solve the rational inequality \(\frac{x^2 - 4}{x^2 - 5x + 6} \geq 0 \)
Converting from Interval to Inequality
Find the interval notation of the solution set of the inequality \(2x^{2} - 5x + 2 > 0\), then convert it into inequality notation.
Finding the Holes in a Graph
Find the holes in the graph of the function \(f(x) = \frac{x^2 - 9}{x - 3}\).