Mathematics, 03.08.2019 15:30 19youngr

How do i find a domain to a piecewise function?

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Answer from: adrian2006

You can find the domain of a piecewise function from the union of all the piece intervals. join all the intervals together (and also consider the domains of the individual pieces).consider the following example: $f(x) = \begin{cases} -5x + 4 & \text{ if } -3 \le x \ \textless \ 2 \\ 6x + 0.2 & \text{ if }2\le x \le 5 \end{cases}$ the domain is the union of the intervals $-3 \le x \ \textless \ 2$ $2 \le x \le 5$ with the union being the interval that contains all the values from both intervals. it joins both intervals together.from the first interval, it says that the domain contains all the values from -3 inclusive to 2 exclusive.from the second interval, it says that the domain also contains all the values from 2 inclusive to 5 inclusive. note that the 2 inclusive makes up for the gap from the previous interval.thus all the values from -3 inclusive to 5 inclusive are in the union, which is the domain. $x \in [-3,5]$ ======consider the following example: $f(x) = \left\{ \begin{array}{ll} 5x^2 & \text{ if } x \ \textless \ 4 \\ x& \text{ if } 4 \ \textless \ x \ \textless \ 5 \\ 5x& \text{ if } 5 \le x \ \textless \ 6\end{array} \right.$ the domain is the union of the intervals $x \ \textless \ 4,\ 4 \ \textless \ x \ \textless \ 5,\ 5 \le x \ \textless \ 6$ which is $x \in (-\infty, 4)\cup(4,6)$ ======consider the following example: $f(x) = \begin{cases} \frac{1}{x} & \text{ if }x \neq 0 \\ -3 & \text{ if } x= 0 \end{cases}$ the domain of this is all real numbers, i.e. $x \in(\infty,\infty)$ the piece $f(x) = \frac{1}{x}$ is is only undefined at x = 0, otherwise it is defined for all real numbers. the piecewise definition fixes this undefined point by defining a value at x = 0.======consider the following example: $g(t) = \begin{cases} -4.2t^2 & \text{ if } -3 \ \textless \ t \ \textless \ 0.5 \\ -t+4 & \text{ if } 0.5 \ \textless \ t \le 5 \\ 5 & \text{ if } t \ \textgreater \ 5 \end{cases}$ the domain of this is $t \in (-3,0.5)\cup(0.5,\infty)$ ======consider the following example: $p(x) = \begin{cases} \frac{1}{x} & \text{ if } -5\le x \le 5 \\ -3 & \text{ if } 5 \ \textless \ x \le 10 \end{cases}$ note that although the piece $p(x) = \frac{1}{x}$ is for $-5\le x \le 5$ , the piece itself is undefined at $x=0$ (division by zero), so that's another domain restriction to consider.domain is $x \in [-5,0)\cup(0, 10]$

Answer from: Quest

X= -5because this is a single step equation so you would just have to divide -16 both sides for x to equal your solution

Answer from: Quest

given : the shape of his satellite can be modeled by where x and y are modeled in inches.

now,the given equation is a equation of parabola.

here, coefficient of x is positive, hence the parabola opens rightwards.

on comparing this equation with standard equation , we get

in standard equation, coordinates of focus=(0,m)

thus for given equation coordinates of focus=(0,1.5)

step-by-step explanation:

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