b Make a table of values and then plot the ordered pairs on the coordinate plane.
C
c Make a table of values and then plot the ordered pairs on the coordinate plane.
D
d Make a table of values and then plot the ordered pairs on the coordinate plane.
E
e Graph each function on the same coordinate plane and compare them.
A
aGraph:
B
bGraph:
C
cGraph:
D
dGraph:
E
e See solution.
Practice makes perfect
a We want to graph the given function.
y = sqrt(4x)
Let's start by finding the domain. To do so, recall that the radicand of a square root is always greater than or equal to 0.
4x≥ 0 ⇒ x ≥ 0
Therefore, the domain of the given function is the set of all positive real numbers. With this in mind, we will make a table of values and then graph the function.
x
sqrt(4x)
y
0
sqrt(4( 0))
0
1
sqrt(4( 1))
2
3
sqrt(4( 3))
≈ 3.5
5
sqrt(4( 5))
≈ 4.5
7
sqrt(4( 7))
≈ 5.3
9
sqrt(4( 9))
6
Now, let's plot these ordered points and connect them with a smooth curve.
b Proceeding in the same way, we will graph the given function.
y = sqrt(5x)
Let's make a table of values and then graph the function.
x
sqrt(5x)
y
0
sqrt(5( 0))
0
1
sqrt(5( 1))
≈ 2.2
3
sqrt(5( 3))
≈ 3.9
5
sqrt(5( 5))
5
7
sqrt(5( 7))
≈ 5.9
9
sqrt(5( 9))
≈ 6.7
By plotting these ordered pairs, we can draw the graph of the function.
c Let's do the same thing for the third function.
y = sqrt(6x)
We will make a table of values.
x
sqrt(6x)
y
0
sqrt(6( 0))
0
1
sqrt(6( 1))
≈ 2.4
3
sqrt(6( 3))
≈ 4.2
5
sqrt(6( 5))
≈ 5.5
7
sqrt(6( 7))
≈ 6.5
9
sqrt(6( 9))
≈ 7.3
Again, we will plot the ordered points and draw the function.
d The last function is different than the others. Note that the coefficient is negative.
y = sqrt(- 6x)
Therefore, its domain will be also different.
- 6x≥ 0 ⇒ x ≤ 0
The domain of this function is the set of all non-positive real numbers. With this in mind, we will make a table of values and then graph the function.
x
sqrt(- 6x)
y
0
sqrt(-6( 0))
0
- 1
sqrt(-6( - 1))
≈ 2.4
- 3
sqrt(-6( - 3))
≈ 4.2
- 5
sqrt(- 6( - 5))
≈ 5.5
- 7
sqrt(- 6( - 7))
≈ 6.5
-9
sqrt(-6( -9))
≈ 7.3
Now, let's plot these ordered points and connect them with a smooth curve.
e We want to know how the graph of y=sqrt(nx) changes as the value of n varies. To think about this, let's plot the all the functions on the same coordinate plane.
We can see that as the value of n increases, the functions horizontally shrink. We can also see that the negative coefficient flips the function over the y-axis. This transformation is a reflection about the y-axis.
