Question

Find domain and range with full steps in copy. Then i will mark brainest.​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Problem 1

Domain = {3, -3, 7, -8}

Range = {7, -2, -5}

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The domain is the set of possible x inputs, while the range is the set of possible y outputs. Toss out any duplicates.

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Problem 2

Domain in words = set of all real numbers

Domain in set builder notation = $\{x|x \in \mathbb{R}\}$

Domain in interval notation = $(-\infty, \infty)$

Range in words = set of real numbers equal to -4 or greater

Range in set builder notation = $\{y|y \in \mathbb{R}, \ y \ge -4\}$

Range in interval notation = $[-4, \infty)$

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I recommend graphing out y = 3x^2-4 to see a parabola in which we can plug in any x value without restriction. The lowest point on this graph is (0,-4) which tells us the smallest value in the range is -4. There is no largest value in the range.

The square bracket for the interval notation range is to indicate to include -4 as part of the interval. In contrast, a curved parenthesis means to exclude the endpoint.

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Problem 3

Domain in words = set of nonzero real numbers

Domain in set builder notation = $\{x|x \in \mathbb{R}, \ x \ne 0\}$

Domain in interval notation = $(-\infty, 0) \cup (0, \infty)$

Range in words = set of nonzero real numbers

Range in set builder notation = $\{y|y \in \mathbb{R}, \ y \ne 0\}$

Range in interval notation = $(-\infty, 0) \cup (0, \infty)$

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The domain and range are the same in this case. Basically x can be anything but zero since you cannot divide by zero. We can show that y = 0 is not possible if we were to find the inverse of y = 2/x getting x = 2/y, so we see that y = 0 would lead to another division by zero error. These domain and range restrictions lead to the vertical and horizontal asymptotes.

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Problem 4

Domain in words = set of real numbers equal to 3 or greater

Domain in set builder notation = $\{x|x \in \mathbb{R}, \ x \ge 3\}$

Domain in interval notation = $[3, \infty)$

Range in words = set of all real numbers

Range in set builder notation = $\{y | y \in \mathbb{R}\}$

Range in interval notation = $(-\infty, \infty)$

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The graph shows the left most point being (3,0). So x = 3 is the smallest x value allowed. There is no max x value assuming the graph continues on forever to the right.

Meanwhile, the range is any possible y value because the graph goes on forever up and down.