a Graph the original flock function by creating a table of values.
B
b Remember that k represents a vertical shift in the absolute value function.
C
c Remember that a represents a vertical shrink or stretch in the absolute value function.
A
aFunction: g(x)=|x|
Graph:
Domain: (-∞, ∞)
Range: [0,∞)
B
bFunction: h(x)=|x|-2
Graph:
Domain: (-∞, ∞)
Range: [-2,∞)
C
cFunction: q(x)=2|x|
Graph:
Domain: (-∞, ∞)
Range: [0,∞)
Practice makes perfect
a The shape of the flock can be modeled by the following absolute value function.
f(x)= a|x- h|+ k
In this function, a represents the growth or shrinkage of the distance between geese, k represents the height change of the flock, and h represents a left or right shift in the flock. Let's graph the original flock function, g(x)=|x|, by creating a table of values.
x
|x|
g(x)
-2
| -2|
2
-1
| -1|
1
0
| 0|
0
1
| 1|
1
2
| 2|
2
Next, we will plot the points and graph the function.
Depending on the graph, we can determine the domain the range as the following.
Domain: &(-∞, ∞)
Range: &[0,∞)
b Since k represents the height of the flock, 2 feet drop can be written as below.
h(x)=|x|-2
In the graph of the function, k represents the vertical shift. Therefore, we will translate the original flock function 2 units down.
We can determine the domain and the range of h(x)=|x|-2 as the following.
Domain: &(-∞, ∞)
Range: &[-2,∞)
c Since a represents the distance between the geese, we will write the function of doubled distance as the following.
q(x)= 2|x|
In the graph of absolute value function, a represents the vertical shrink or stretch. Therefore, we will stretch the original flock function by a factor of 2.
The domain and the range can be written as same as in Part A.
Domain: &(-∞, ∞)
Range: &[0,∞)
