Determining if the Point is on the Graph
Given the function \(f(x) = x^3 + 2x^2 - x + 2\), determine if the point \((2,14)\) is on the graph of this function.
Find the Behavior (Leading Coefficient Test)
Determine the end behavior of the function \(f(x) = -3x^4 + 2x^2 - 1\) using the Leading Coefficient Test
Determining Odd and Even Functions
Determine whether the function \(f(x) = x^4 - 2x^2 + 1\) is odd, even, or neither.
Finding the Symmetry
Determine whether the function \(f(x) = x^4 - 4x^2 + 1\) is symmetric about the y-axis, the origin, or neither.
Finding the Asymptotes
Find the vertical and horizontal asymptotes of the function \( f(x) = \frac{3x^2 - 2x + 1}{x^2 - 1} \).
Difference Quotient
Find the difference quotient for the function \(f(x) = 3x^2 - 2x + 1\).
Finding the Antiderivative
Find the antiderivative of the function \(f(x) = 3x^2 - 5x + 7\).
Graphing
Find the maximum and minimum points on the graph of the function \(f(x) = x^3 - 6x^2 + 9x + 15\).