Interpret Absolute Value Functions as Piecewise
Read this topicExplanations 3
- (Video) Writing an Absolute Value as a Piecewise Function by Daniel Kopsas This video by Daniel Kposas explains the connection between absolute values and piecewise functions. S…
By Ben Ferrara, Zora Gilbert, Alex Federspiel, Ruiran Xun, Amy Feraco, Jonathan Heller, Dani, Anusha Rahman
- Split the equation into pieces Before we go into solving absolute value as a piecewise function, let's first look at piecewise functions! Piecewise functions are functions that …
By Zora Gilbert, Alex Federspiel, Joshua Siktar, Ruiran Xun, Jonathan Heller, Dani, Anusha Rahman
- Interpret Absolute Value Functions as Piecewise When interpreting an absolute value function as a piecewise function (which could be helpful for graphing), it is important to re…
By Caroline K
Problems 20
- What would the piecewise function: y={x−2if x≥2−(x−2)if x<2y=\left\{\begin{matrix} x-2 & \text{if }x\geq2\\-(x-2) &\text{if } x<2\end{matrix}\right.y={x−2−(x−2)if x≥2if x<2 lo…
- What would the piecewise function: y={x+3 if x≥0−x+3 if x<0y=\left\{\begin{matrix} x+3\,\,\,\,\text{if}\,\,\,\,x\geq0\\-x+3\,\,\,\,\text{if}\,\,\,\,x<0\end{matrix}\right.y={x+3i…
- What would the piecewise function: y={−2x−6 if −2x≥02x−6 if −2x<0y=\left\{\begin{matrix} -2x-6\,\,\,\,\text{if}\,\,\,\,-2x\geq0\\2x-6\,\,\,\,\text{if}\,\,\,\,-2x<0\end{matrix}\r…
- What would the piecewise function: y={x−7 if x−7≥0−x+7 if x−7<0y=\left\{\begin{matrix} x-7\,\,\,\,\text{if}\,\,\,\,x-7\geq0\\-x+7\,\,\,\,\text{if}\,\,\,\,x-7<0\end{matrix}\right…
- What does the absolute value function y=∣3x∣y=|3x|y=∣3x∣ look like as a piecewise function?
- What does the absolute value function y=∣x+4∣y=|x+4|y=∣x+4∣ look like as a piecewise function?
- If f(x)={3x+1when x≥02x−1when x<0,f(x)=\begin{cases} 3x+1 & \text{when }x\geq0\\2x-1 &\text{when } x<0\end{cases},f(x)={3x+12x−1when x≥0when x<0, find f(3)f(3)f(3) and f(−1)f(…
- You have a job that pays you double for each hour worked overtime. Overtime is considered over 505050 hours. After 505050 hours, the hourly rate is double that of 7\77 per hour.
- Consider the graph above. Which function represents y=∣x∣y=|x|y=∣x∣ and which function represents y=−∣x∣y=-|x|y=−∣x∣?
- When evaluating piecewise functions, the first step is to always:
- Define f(⋄)=∣⋄∣f(\diamond)=|\diamond|f(⋄)=∣⋄∣ as a piecewise function.
- Consider the function f(x)=∣x−2∣+1f(x)=\left|x-2\right|+1f(x)=∣x−2∣+1. Which of the following equations shows where the graph is sloped negatively?
- Which of the following piecewise functions does the graph above represent?
- Which of the following is NOT true for the function f(x)=∣x∣f\left(x\right)=\left|x\right|f(x)=∣x∣?
- The absolute value function is commonly used to determine the ______ between two numbers on the number line.
- Write f(x)=∣x−4∣f(x)=|x-4|f(x)=∣x−4∣ as a piecewise defined function.
- Write f(x)=∣2x−10∣+2f(x)=|2x-10|+2f(x)=∣2x−10∣+2 as a piecewise defined function.
- If yyy is the following piecewise function, where kkk is a constant, what would yyy be as an absolute value function? y={kxifkx≥0−kxifkx<0y = \bigg\{ \begin{array}{ccc} kx & \te…
- What absolute value function does the following piecewise function represent? f(x)={4x+1 if 4x+1≥0−4x−1 if 4x+1<0f(x) = \begin{cases} \begin{align} 4x+1 \quad \text{ if }& \quad…
- What values of aaa and bbb would make this piecewise function into an absolute value function? y={5x+5 if 5x≥3ax+b if 5x<3y=\left\{\begin{matrix} 5x+5\;\;\text{if}\;\;5x\geq3\\a…