Create two tables of values and then plot the graphs on the same coordinate plane.
Graph:
Comparison: See solution.
Practice makes perfect
To graph the functions without going through the entire process of transforming the parent function, we can make two tables of values. Then we only need to plot the ordered pairs that we find.
Graph
Let's begin with creating a table of values for c(x).
x
4|x+3|-1
Simplify
c(x)
-5
4| -5+3|-1
4|-2|-1
7
-4
4| -4+3|-1
4|-1|-1
3
-3
4| -3+3|-1
4|0|-1
-1
-1
4| -1+3|-1
4|2|-1
7
Now we will do the same with d(x).
x
-4/3|x+3|+1/3
Simplify
d(x)
-4
-4/3| -4+3|+1/3
-4/3|-1|+1/3
-1
-3
-4/3| -3+3|+1/3
-4/3|0|+1/3
1/3
-2
-4/3| -2+3|+1/3
-4/3|1|+1/3
-1
-1/2
-4/3| -1/2+3|+1/3
-4/3|5/2|+1/3
-3
Finally, we can take these ordered pairs and plot them on one coordinate plane.
Comparison
Notice from the graphs that d(x) is a vertical shrink by a factor of 13, reflection in the x-axis, and a vertical translation 1 13 units up of the graph of c(x).
