1. The range of the given function y = 3x² for the given domain: {- 2, - 1, and 0} is {12, 3, 0}.
2. The range of the given function y = 8x + 1, where x > 2 is (17, ∞).
3. The range of the given function y = 5x + 2, where x > -2 is (- 8, ∞).
We know that the range of a function is the entire set of all possible values for the dependent variable (typically y), after substituting the domain.
1. For the function y = 3x²,
Here the domain is {- 2, - 1, and 0}. So, we have to find the y values for the x values - 2, - 1, and 0 to find the range of the function.
Now, at x = - 2,
y = 3(- 2)² = 3 × 4 = 12
At x = - 1,
y = 3(- 1)² = 3 × 1 = 3
At x = 0,
y = 3(0)² = 3 × 0 = 0
So, the range of this function is {12, 3, 0}.
2. Now, for the function y = 8x + 1,
At x = 2,
y = 8 × 2 + 1 = 16 + 1 = 17
Since the domain is x > 2, we can say that the range set will contain values greater than 17.
So, the range of this function is (17, ∞).
3. For the function y = 5x + 2,
Now, at x = - 2,
y = 5 × (- 2) + 2 = - 10 + 2 = - 8
Since the domain is x > - 2, we can say that the range set will contain values greater than - 8.
So, the range of this function is (-8, ∞).
1. Therefore, the range of the given function y = 3x² for the given domain: {- 2, - 1, and 0} is {12, 3, 0}.
2. The range of the given function y = 8x + 1, where x > 2 is (17, ∞).
3. The range of the given function y = 5x + 2, where x > -2 is (- 8, ∞).
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