Question

Which graph represents the function?



f(x)=⎧⎩⎨⎪⎪(x+2)2ifx<−1∣∣x∣∣+1if−1≤x≤1−x√ifx>1

Answer 1

Answer:

See graph.

Step-by-step explanation:

Look for the pattern of the quadratic graph,

$f(x)=(x+2)^2$ on the interval $x\:<\:-1$.

This is the graph of the parent function $f(x)=x^2$ shifted 2 units to the left.

On the interval $-1\le x\le 1$, look for the pattern of the absolute value function $f(x)=|x|+1$.

This is the graph of the parent function, $f(x)=|x|$ shifted up 1 unit.

On the interval $x\:>\:1$, look for the pattern of the square root function, $f(x)=-\sqrt{x}$.

This is a reflection of the graph of the parent function, $y=\sqrt{x}$ reflected in the x-axis.