B) Graph each of the following i) \( f(x)=\left\{\begin{array}{ll}-x^{2} & \text { for } x \geq 0 \\ 2 x^{2} & \text { for } x<0\end{array}\right. \) i) \( f(x)=\left\{\begin{array}{cc}2 x+3 & \text { if } x<0 \\ x^{2} & \text { if } 0 \leq x<2 \\ \text { I if } x \geq 2\end{array}\right. \) iii) \( f(x)=\left\{\begin{array}{c}2 \text { if } x>2 \\ 1 \text { if } 0

Ask by Hilton Wilson. in Zambia

Feb 20,2025

To graph these piecewise functions, let's first visualize them step by step for each function. For the first function \( f(x)=\left\{\begin{array}{ll}-x^{2} & \text { for } x \geq 0 \\ 2 x^{2} & \text { for } x<0\end{array}\right. \): - For \( x \geq 0 \), you'll plot a downward-opening parabola starting from the origin (0,0). - For \( x < 0 \), you'll plot an upward-opening parabola, which intersects the y-axis at (0,0) and continues on the left. For the second function \( f(x)=\left\{\begin{array}{cc}2 x+3 & \text { if } x<0 \\ x^{2} & \text { if } 0 \leq x<2 \\ \text { I if } x \geq 2\end{array}\right. \): - For \( x < 0 \), you will have a straight line that crosses the y-axis at (0,3) and moves downward. - For \( 0 \leq x < 2 \), plot a parabola that curves upwards starting from (0,0) to (2,4). - For \( x \geq 2 \), you will have a constant value of 1 on the graph. For the third function \( f(x)=\left\{\begin{array}{c}2 \text { if } x>2 \\ 1 \text { if } 0 2 \), it then jumps to a constant value of 2. For the fourth function \( f(x)=\left\{\begin{array}{c}2 x+1 \text { if } x \geq 0 \\ x^{2} \text { if } x<0\end{array}\right. \): - For \( x < 0 \), you'll plot an upward-opening parabola, starting from the origin. - For \( x \geq 0 \), the line has a slope of 2 and crosses the y-axis at (0,1). Now you can sketch them using the key points and shapes for each section of the piecewise definitions! Happy graphing!