f(x)=x^2-4

Frequently Asked Questions

• Find the vertex of \(f(x)=x^2-4\)

  

  $$\left(0,-4\right)$$

• Find the axis of symmetry of \(f(x)=x^2-4\)

  

  $$x=0$$

• Evaluate the derivative of \(f(x)=x^2-4\)

  

  $$f^{\prime }\left(x\right)=2x$$

• Find the domain of \(f(x)=x^2-4\)

  

  $$x\in \mathbb{R}$$

• $$\text{Find the }x\text{-intercept/zero}$$ of \(f(x)=x^2-4\)

  

  $$x_1=-2,x_2=2$$

• Find the y-intercept of \(f(x)=x^2-4\)

  

  $$f\left(0\right)=-4$$

• Find the critical numbers of \(f(x)=x^2-4\)

  

  $$x=0$$

• Find the local extrema of \(f(x)=x^2-4\)

  

  $$\begin{array}{rl}& \text{The local minimum is}-4\text{at}x=0\end{array}$$

• Find the increasing or decreasing interval of \(f(x)=x^2-4\)

  

  $$\begin{array}{rl}& \text{The increasing interval is}x\ge 0\\ & \text{The decreasing interval is}x\le 0\end{array}$$

• Find the range of \(f(x)=x^2-4\)

  

  $$f\left(x\right)\ge -4$$

• Find the vertical asymptotes of \(f(x)=x^2-4\)

  

  $$\text{No vertical asymptotes}$$

• Find the horizontal asymptotes of \(f(x)=x^2-4\)

  

  $$\text{No horizontal asymptotes}$$

• Find the oblique asymptotes of \(f(x)=x^2-4\)

  

  $$\text{No oblique asymptotes}$$

• Determine if even, odd or neither of \(f(x)=x^2-4\)

  

  $$\text{Even}$$

• Find the stationary points of \(f(x)=x^2-4\)

  

  $$\left(0,-4\right)$$

• Find the inflection points of \(f(x)=x^2-4\)

  

  $$\text{No inflection points}$$

• Testing for symmetry about the origin of \(f(x)=x^2-4\)

  

  $$\text{Not symmetry with respect to the origin}$$

• Testing for symmetry about the x-axis of \(f(x)=x^2-4\)

  

  $$\text{Not symmetry with respect to the x-axis}$$

• Testing for symmetry about the y-axis of \(f(x)=x^2-4\)

  

  $$\text{Symmetry with respect to the y-axis}$$