Sketch the graph of the function. $$f ( x ) = \left\{ \begin{array} { l l c } - x & \text { if } \quad x 1 \end{array} \right.$$ E) none

Question

Sketch the graph of the function. $$f ( x ) = \left\{ \begin{array} { l l c } 
- x & \text { if } \quad x < - 1 \
x ^ { 2 } & \text { if } & - 1 \leq x \leq 1 \
1 & \text { if } & x > 1
\end{array} \right.$$
E) none

Quizplus · Accepted Answer

For $x<-1$, $f(x)=-x$ which is the graph of $y=-x$ reflected around the $y$-axis.
For $-1\leq x\leq 1$, $f(x)=x^2$ which is a parabola that opens upwards and has its vertex at $(0,0)$.
For $x>1$, $f(x)=1$ which is a horizontal line passing through $(1,1)$.
Therefore, the graph of $f(x)$ is like below. 
[asy]
import graph; size(200); 
real ticklen=3;
real tickspace=2;

real f(real x)
{
  if (x < -1){return (-x);}
  else if( x <=1 ){return x^2;}
  else{return 1;}
}

real xMin=-3;
real xMax=3;
real yMin=-1;
real yMax=3;

real[] xTicks={-2,-1, 0, "1",2};
real[] yTicks={-1,0,1,2};

draw(graph(f,xMin,-1.01),red);
draw(graph(f,-1,1),red);
draw(graph(f,1,xMax),red);

ylimits(yMin,yMax);
xlimits(xMin,xMax);
draw(xaxis(ticks=xTicks,above=true), black+linewidth(1));
draw(yaxis(ticks=yTicks,Arrows(4),above=true), black+linewidth(1));
[/asy]

Sketch the Graph of the Function A) B) C) D)

Sketch the Graph of the Function A)

B)

C)

D)