1. The problem asks to create a piecewise function that includes at least one absolute value and then graph it. 2. A piecewise function is defined by different expressions depending on the input value $x$. The absolute value function is defined as $|x| = \begin{cases} x & \text{if } x \geq 0 \\ -x & \text{if } x < 0 \end{cases}$. 3. Let's define the piecewise function: $$f(x) = \begin{cases} |x| & \text{if } x < 2 \\ 3x - 4 & \text{if } x \geq 2 \end{cases}$$ 4. For $x < 2$, the function outputs the absolute value of $x$, which means it outputs $x$ if $x$ is positive or zero, and $-x$ if $x$ is negative. 5. For $x \geq 2$, the function outputs the linear expression $3x - 4$. 6. This function is continuous at $x=2$ because: $$\lim_{x \to 2^-} f(x) = |2| = 2$$ $$f(2) = 3(2) - 4 = 6 - 4 = 2$$ 7. The graph will show the absolute value function for $x < 2$ and the line $3x - 4$ for $x \geq 2$. Final answer: $$f(x) = \begin{cases} |x| & x < 2 \\ 3x - 4 & x \geq 2 \end{cases}$$