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Aleonysh [2.5K]
2 years ago
9

Really easy please help me

Mathematics
2 answers:
natka813 [3]2 years ago
5 0
Need a picture or a problem then we can help
DIA [1.3K]2 years ago
4 0
We need a picture, then we can help you with the problem.
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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
Whih of the following is equivalent to (81m^6)^1/2
Setler [38]
Can you list the answer choices?

\sqrt{81m^6}   would be equivalent
4 0
3 years ago
Read 2 more answers
What is 5/8 written as a decimal and a percent?
grandymaker [24]
Im not sure about the percent but as a decimal its <em><u>1.6</u></em>
3 0
3 years ago
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A ball is thrown upward off of a 100 meter cliff with an initial velocity of 6 m/s. The function f(x)=-5x2+6x+100 (graphed below
Troyanec [42]

Answer:

E

Step-by-step explanation:

A ball is thrown upward off of a 100 meter cliff with an initial velocity of 6 m/s. The function f(x)=-5x2+6x+100 (graphed below) represents this situation where x is time and y is the distance off of the ground.

e. What would the new function be? What kind of transformation is this?

f. Would you still use the same domain and range? Why or why not?

8 0
3 years ago
Directions:Find the solution of the follow equations and check your work
Mekhanik [1.2K]

y=28×9

=252

x=334-150

=184

h=254×100

=25400

Step-by-step explanation:

to check the equations substitute the values by the variables

7 0
2 years ago
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