Given a piecewise function:
![f(x) = \left\{ \begin{array}{rcl} 3x-5} & \mbox{if} & x \leq-1 \\ -2x+3 & \mbox{if} & -1 < x < 4 \\ {2} & \mbox{if} &x \geq4 \end{array}\right.](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cleft%5C%7B%20%5Cbegin%7Barray%7D%7Brcl%7D%203x-5%7D%20%26%20%5Cmbox%7Bif%7D%20%26%20x%20%5Cleq-1%20%5C%5C%20-2x%2B3%20%26%20%5Cmbox%7Bif%7D%20%26%20-1%20%3C%20x%20%3C%204%20%5C%5C%20%7B2%7D%20%26%20%5Cmbox%7Bif%7D%20%26x%20%5Cgeq4%20%5Cend%7Barray%7D%5Cright.)
To graph the function follow the steps below:
<h3>Step 1</h3>
Graph the first function, f(x) = 3x - 5
Plot two points with x- coordinates - 1 and 0. We considered x ≤ -1 when selecting points.
- f(-1) = 3(-1) - 5 = - 8
- f(-2) = 3(-2) - 5 = - 11
Make point (- 1, - 8) a full dot and connect two points, then extend the line to the left from x = -2.
<h3>Step 2</h3>
Graph the second function, f(x) = - 2x + 3.
Plot both endpoints with x - coordinates of - 1 and 4.
- f(-1) = - 2(-1) + 3 = 5
- f(4) = - 2(4) + 3 = - 5
Make both points (-1, 5) and (4, 5) open dots and connect together.
<h3>Step 3</h3>
Graph the third function, f(x) = 2.
Every point of this function has the value of 2, we are interested in the endpoint when x = 4.
Make this point a full dot and make a line parallel to the x-axis, to the right from the plotted point.
Now we have the full graph, <u>see attached</u>.
Sort the data from the smallest one.
42, 55, 69, 74, 78, 83, 83, 97, 99
There are 9 data, n = 9
Find the location of Q₂
Q₂ location = (n + 1)/2
Q₂ location = (9 + 1)/2
Q₂ location = 10/2
Q₂ location = 5
The location of Q₂ is in the fifth order
42 first order
55 second order
69 third order
74 fourth order
78 fifth order
etc
So the Q₂ or the median is 78
It should be 192 I’m pretty sure
<u>Answer:</u>
or ![1 . 1 1 1](https://tex.z-dn.net/?f=%201%20.%201%201%201%20)
<u>Step-by-step explanation:</u>
We are given the following two fractions that we are to divide:
÷
We can rewrite this as:
![= \frac {\frac { 5 } { 1 2 } } {\frac { 3 } { 8 } }](https://tex.z-dn.net/?f=%3D%20%5Cfrac%20%7B%5Cfrac%20%7B%205%20%7D%20%7B%201%202%20%7D%20%7D%20%7B%5Cfrac%20%7B%203%20%7D%20%7B%208%20%7D%20%7D)
To change this division into multiplication, we will take the reciprocal of the fraction in the denominator to get:
or ![1 . 1 1 1](https://tex.z-dn.net/?f=%201%20.%201%201%201%20)