Chapter Test
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Create one piece that has the required range. Add horizontal lines to the left and to the right of it.
Example Solution:
y=
0,&x<0
- x+1,& 0≤ x<4
0,& x≥4
Note that there is an infinite number of solutions to this exercise. This is just one possibility to help visualize the process. We will solve this by first creating one piece of the function that has the required range. Then we will add two pieces to ensure that the function have a domain of all real numbers.
We want the range of the function to be -3
Slope=Δ y/Δ x ⇒ Slope=- 1/1= - 1 We find the equation of the line by substituting these values into the slope-intercept form of a line. y= mx+ b ⇒ y= - 1x+ 1 Let's simplify the expression and add that its domain is 0≤ x < 4. y= - 1x+ 1,& 0≤ x < 4 ⇕& y=- x+1,& 0≤ x < 4
We now have to add one piece to the left and one piece to the right of the line we already have. Let's recall the requirements for the function.
These two pieces must ensure that the domain becomes all real numbers without changing the range. We can do that by making the left and right piece horizontal lines. Let's graph an example of how these pieces can look.
Notice that the left piece ends with an open circle and that the right piece ends with a closed circle. We can now write the equation of the function. y= 0,&x<0 - x+1,& 0≤ x<4 0,& x≥4