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The domain of a function is the set of the possible values of x, while the range of a function is the set of the resulting values of the functions from the domain.
By inspection it can be seen that the function
f(x) = 4 - 4x has the domain and range as follows:
<span>domain: {0, 1, 3, 5, 6}
range: {-20, -16, -8, 0, 4}
i.e. 4 - 4(0) = 4 - 0 = 4
4 - 4(1) = 4 - 4 = 0
4 - 4(3) = 4 - 12 = -8
4 - 4(5) = 4 - 20 = -16
4 - 4(6) = 4 - 24 = -20
Also, the function
f(x) = 5x - 3 has the domain and range as follows:
</span><span>domain: {-2, -1, 0, 3, 4}
range: {-13, -8, -3, 12, 17}
i.e. 5(-2) - 3 = -10 - 3 = -13
5(-1) - 3 = -5 - 3 = -8
5(0) - 3 = 0 - 3 = -3
5(3) - 3 = 15 - 3 = 12
5(4) - 3 = 20 - 3 = 17
Also, the function
f(x) = -10x has the domain and range as follows:
</span><span>domain: {-4, -2, 0, 2, 4}
range: {-40, -20, 0, 20, 40}
i.e. -10(-4) = 40
-10(-2) = 20
-10(0) = 0
-10(2) = -20
-10(4) = -40
Also, the function
has the domain and range as follows:
</span><span>domain: {-3, -2, -1, 2, 6}
range: {0.5, 0, -1.5, 3, 2}
i.e.
</span>
By inspection it can be seen that the function
f(x) = 4 - 4x has the domain and range as follows:
<span>domain: {0, 1, 3, 5, 6}
range: {-20, -16, -8, 0, 4}
i.e. 4 - 4(0) = 4 - 0 = 4
4 - 4(1) = 4 - 4 = 0
4 - 4(3) = 4 - 12 = -8
4 - 4(5) = 4 - 20 = -16
4 - 4(6) = 4 - 24 = -20
Also, the function
f(x) = 5x - 3 has the domain and range as follows:
</span><span>domain: {-2, -1, 0, 3, 4}
range: {-13, -8, -3, 12, 17}
i.e. 5(-2) - 3 = -10 - 3 = -13
5(-1) - 3 = -5 - 3 = -8
5(0) - 3 = 0 - 3 = -3
5(3) - 3 = 15 - 3 = 12
5(4) - 3 = 20 - 3 = 17
Also, the function
f(x) = -10x has the domain and range as follows:
</span><span>domain: {-4, -2, 0, 2, 4}
range: {-40, -20, 0, 20, 40}
i.e. -10(-4) = 40
-10(-2) = 20
-10(0) = 0
-10(2) = -20
-10(4) = -40
Also, the function
</span><span>domain: {-3, -2, -1, 2, 6}
range: {0.5, 0, -1.5, 3, 2}
i.e.
The graph of the function:
Is the last graph (bottom graph of the second image).
<h3>Which graph represents the given function?</h3>
Here we have the function:
Remember that the argument of a square root must be zero or larger, then the minimum of the domain is the value of x such that:
x + 2 = 0
x = -2
Then the function starts at:
Then the graph should start at (-3, 2).
We can also identify another point by evaluating in x = 2.
So the function also passes through (2, - 1).
Notice that the only graph that contains these two points is the last graph (the bottom graph on the second image), so that is the correct option.
If you want to learn more about square roots:
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