Graph the piecewise function 𝑓(x) = { 4 if x<1, |x-2| if -1≤x<3, { 2x-5 if x≥3

Question

Graph the piecewise function 𝑓(x) = { 4 if x<1

{ |x-2| if -1≤x<3

{ 2x-5 if x≥3

below. Remember to label your axes and show your scale. Give intervals where the graph is increasing, decreasing and constant.

please help solve!

Answer 1

I've created a solution assuming that the first function should have been x < -1 as would make more sense based on the context of the other functions.

A piecewise function means the function is in "pieces" or segments to be drawn mostly independently of each other.

1. The first function indicates that y = 4 coming from negative infinity all the way to -1 and is therefore a straight, horizontal line. However, since x < -1, -1 cannot be included in our answer and should be left with a "hole" at that end of our line. The value for x = -1 will be computed as part of the next function.
2. The second function indicates that y = | x - 2 | from -1 to 3, not including 3. However, we should still find what the value "would be" if 3 were included to create a complete graph. Simply calculate the values of y for each of the whole numbers between -1 and 3. (There are better ways to solve absolute value problems, but plugging in only 5 numbers in this case is faster.) Plot these points on the graph, then connect the dots. Make sure that this does not include the final value for x = 3 as part of this graph.
3. The third function indicates that y = 2x - 5 starting at x = 3 and going to positive infinity. This function is given in slope-intercept form, making for easy graphing. To further simplify, I plugged in x = 3 and used that value of y as my starting point. Then, I simply used the slope of 2/1 (remember slope is rise/run) that was indicated by the 2 in the equation to plot further points in the line.

Once you've followed these three steps, you'll have solved the graph. Here's what mine ended up looking like: https://1drv.ms/u/s!ApWIaKiDDnULrfZvrpoEo0e15Qlgmg?e=0zVS7D