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scZoUnD [109]
3 years ago
12

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

Mathematics
2 answers:
nikklg [1K]3 years ago
6 0

Answer:

Step-by-step explanation:

Ymorist [56]3 years ago
5 0

Problem 1

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

Range = {7, -2, -5}

----------

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

===================================================

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)

----------

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.

===================================================

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)

----------

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.

===================================================

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)

----------

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.

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