Piecewise Linear Functions
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- (Video) PIecewise Linear Functions by Kirk Weiler Here's a video by Kirk Weiler going over piecewise linear functions. He works through some common problems involving the topic.…
By Alex Federspiel, Anusha Rahman
- Curve Approximations We often learn about slope by studying linear functions. Early in algebra, you learn how to graph lines using slope-intercept form and point-slope form. But…
By Jonathan Heller, Anusha Rahman
- Piecewise Linear Functions A linear piecewise function is a function made up of different lines. Each line works over a specific interval of input values. This means one rule ap…
By Anusha Rahman
Problems 20
- Which of the following can be graphs of piecewise linear functions?
- True or False\text{True or False}True or False === The function {3x+6x≤−35−3<x<0−2x+50≤x<14x−121≤x<43−20x+1643≤x\\\begin{cases} 3x+6&x\leq-3\\ 5&-3<x<0\\ -2x+5&0\leq x<1\\ 4x-12…
- True or False\text{True or False}True or False === If a graph is made up of different linear functions, then it, as a whole, is linear.
- A train is traveling a total of 868686 miles today. The train travels 282828 miles in the first 141414 minutes of the trip. The train then slows down due to weather conditions. …
- Graph the following. f(x)={12x−4−2≤x≤5−2x+125<x≤9f(x)=\begin{cases} \frac{1}{2}x-4&-2\le{x}\le{5}\\ -2x+12&5<x\le{9} \end{cases}f(x)={21x−4−2x+12−2≤x≤55<x≤9 What is the range?
- Find the zero that applies to the interval (5,9](5,9](5,9] inside the domain of the function f(x)={12x−4−2<x≤5−2x+125<x≤9f(x)=\begin{cases} \frac{1}{2}x -4&-2<x\le5\\ -2x+12&5<x…
- What are the viable zeros of the following equation: f(x)={x−6≤x≤−218x−13−2<x<3−12x+43≤x≤5f(x)=\begin{cases} x&-6\le{x}\le{-2}\\ \frac{1}{8}x-\frac{1}{3}&-2<x<3\\ -\frac{1}{2}x+…
- Joey's favorite thing to do at the pool is jump off of the diving board. The graph above shows his movements at the pool. The xxx-axis is time in seconds and the yyy-axis is hei…
- Given the function below, which of the following table of values is correct? f(x)={20≤x≤2−x+32<x≤4−24<x≤6x−76<x≤932x−169<x≤13f(x)=\begin{cases} 2&0\le {x}\le{2}\\ -x+3&2<x\le{4}…
- Parking garages often offer different prices based on how long you are parked. There is an hourly rate of 555 dollars per hour; however, if you are parked for 555 or more hours …
- True or False\text{True or False}True or False === The following function is continuous. f(x)={x+3−12≤x≤−23x+7−2<x≤4f(x)=\begin{cases} x+3&-12\le{x}\le{-2}\\ 3x+7&-2<x\le{4} \en…
- True or False\text{True or False}True or False === The following function is continuous. f(x)={x+3−12≤x≤43x4<x≤14f(x)=\begin{cases} x+3&-12\le{x}\le{4}\\ 3x &4<x\le{14} \end{cas…
- Which of the above piecewise functions are piecewise linear?
- Which of the following piecewise functions are piecewise linear?
- What value of aaa would make the following linear piecewise function continuous? f(x)={−x−2−10≤x≤012x+a0<x≤10f(x)=\begin{cases} -x-2 &-10\le{x}\le{0}\\ \frac{1}{2}x+a &0<x\le{10…
- What value of aaa would make the following linear piecewise function continuous? f(x)={−2x+2−10≤x≤−1227x+a−12<x≤10f(x)=\begin{cases} -2x+2 &-10\le{x}\le{-\frac{1}{2}}\\ \frac{2}…
- Which of the following linear piecewise functions are graphed above?
- Graph the following function. f(x)={x−10≤y≤313x+533<y≤10−x+10<y≤11f(x)=\begin{cases} x-1&0\le{y}\le{3}\\ \frac{1}{3}x+\frac{5}{3}&3<y\le{10}\\ -x+1&0<y\le{11}\\ \end{cases}f(x)=…
- Which of the following could graphed with linear piecewise equations?
- Jerry cuts his grass every Sunday. What is a possible function that represents the grasses growth in inches during a month (303030 days)?