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I am Lyosha [343]
3 years ago
6

What's the answer????

Mathematics
1 answer:
katrin2010 [14]3 years ago
7 0
A
C
D
E
F

B should be the obvious no-no
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1. Write the equation of the piece-wise function graphed below​.
DaniilM [7]

Problem 4

<h3>Answer:</h3>

f(x) = \begin{cases}2x+4 \text{ if } x < 1\\x-3 \text{ if } x \ge 1\end{cases}

------------------

Work Shown:

The left line goes through (-2,0) and (0,4)

The slope of this line is

m = (y2-y1)/(x2-x1)

m = (4-0)/(0-(-2))

m = (4-0)/(0+2)

m = 4/2

m = 2

The y intercept is b = 4

Since m = 2 and b = 4, this means y = mx+b turns into y = 2x+4. This portion is only done when x < 1. Note the open circle at the endpoint of this portion. So we do not include x = 1 as part of this piece.

---

The line on the right side goes through (1,-2) and (2,-1)

Slope

m = (y2-y1)/(x2-x1)

m = (-1-(-2))/(2-1)

m = (-1+2)/(2-1)

m = 1/1

m = 1

The y intercept is b = -3. You can see this if you extend the line until it crosses the y axis.

Alternatively, plug in (x,y) = (1,-2) and m = 1 into y = mx+b to find that b = -3

So y = mx+b turns into y = 1x+(-3) or just y = x-3

We combine both parts to end up with f(x) = \begin{cases}2x+4 \text{ if } x < 1\\x-3 \text{ if } x \ge 1\end{cases}

This is only graphed when x \ge 1 (note the closed or filled in circle for the endpoint of this portion).

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

Problem 5

Answer:

<h3>f(x) = \frac{1}{2}|x+3| is the absolute value function</h3><h3>while this is the piecewise function</h3>

f(x) = \begin{cases}-\frac{1}{2}(x+3) \text{ if } x < -3\\\frac{1}{2}(x+3) \text{ if } x \ge -3\end{cases}\\

------------------

Work Shown:

y = |x| .... parent function

y = |x+3| ... shift 3 units to the left

y = (1/2)*|x+3| .... vertically compress by factor of 1/2

f(x) = (1/2)*|x+3|

------

Break that down into a piecewise function

when x < -3, then y = -(1/2)(x+3)

when x \ge -3, then y = (1/2)(x+3)

I'm using the rule that y = |x| turns into y = -x when x < 0 and y = x when x \ge 0

So that is how we get f(x) = \begin{cases}-\frac{1}{2}(x+3) \text{ if } x < -3\\\frac{1}{2}(x+3) \text{ if } x \ge -3\end{cases}\\as the piecewise function.

8 0
3 years ago
Read 2 more answers
I need help with these problems, thanks
scZoUnD [109]

Answer:

Dr hmm fruncfyhn

Step-by-step explanation:

fudjcjdh FC hey DC KFC TV HD hmm vuejcwsm t Ufa hmm c CT DC x GB chv

7 0
2 years ago
Check the photo pls. If u want to.
Studentka2010 [4]

Answer:

okay

Step-by-step explanation:

8 0
2 years ago
Solve. 3p + 13 = 37 Enter your answer in the box. p =
Sonja [21]
3p = 37-13
3p = 24
3p/3 = 24/3
p = 8
4 0
3 years ago
Read 2 more answers
PLEASE HELP! I NEED THE ANSWERS TODAY
Katen [24]

Answer:

36\sqrt{2}

Explanation:

This radical can be simplified.  You know that the number inside of the radical; 8, is the product of 4 and 2.  You know that 4 is a perfect square (2 times 2).  Therefore, you can leave the 2 on the inside and the 4 on the outside.  You now must multiply the 18 on the outside of the radical by 2 because you must take the square root of the original 4 you had.  Therefore, you answer will be 36\sqrt{2}.

8 0
3 years ago
Read 2 more answers
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