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slega [8]
3 years ago
7

Pls answer asap!!!!!!

Mathematics
1 answer:
Firlakuza [10]3 years ago
7 0

Answer:

Step-by-step explanation:

 

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PLEASE HELP 100 POINTS!!!!!!
horrorfan [7]

Answer:

A)  See attached for graph.

B)  (-3, 0)  (0, 0)  (18, 0)

C)   (-3, 0) ∪ [3, 18)

Step-by-step explanation:

Piecewise functions have <u>multiple pieces</u> of curves/lines where each piece corresponds to its definition over an <u>interval</u>.

Given piecewise function:

g(x)=\begin{cases}x^3-9x \quad \quad \quad \quad \quad \textsf{if }x < 3\\-\log_4(x-2)+2 \quad  \textsf{if }x\geq 3\end{cases}

Therefore, the function has two definitions:

  • g(x)=x^3-9x \quad \textsf{when x is less than 3}
  • g(x)=-\log_4(x-2)+2 \quad \textsf{when x is more than or equal to 3}

<h3><u>Part A</u></h3>

When <u>graphing</u> piecewise functions:

  • Use an open circle where the value of x is <u>not included</u> in the interval.
  • Use a closed circle where the value of x is <u>included</u> in the interval.
  • Use an arrow to show that the function <u>continues indefinitely</u>.

<u>First piece of function</u>

Substitute the endpoint of the interval into the corresponding function:

\implies g(3)=(3)^3-9(3)=0 \implies (3,0)

Place an open circle at point (3, 0).

Graph the cubic curve, adding an arrow at the other endpoint to show it continues indefinitely as x → -∞.

<u>Second piece of function</u>

Substitute the endpoint of the interval into the corresponding function:

\implies g(3)=-\log_4(3-2)+2=2 \implies (3,2)

Place an closed circle at point (3, 2).

Graph the curve, adding an arrow at the other endpoint to show it continues indefinitely as x → ∞.

See attached for graph.

<h3><u>Part B</u></h3>

The x-intercepts are where the curve crosses the x-axis, so when y = 0.

Set the <u>first piece</u> of the function to zero and solve for x:

\begin{aligned}g(x) & = 0\\\implies x^3-9x & = 0\\x(x^2-9) & = 0\\\\\implies x^2-9 & = 0 \quad \quad \quad \implies x=0\\x^2 & = 9\\\ x & = \pm 3\end{aligned}

Therefore, as x < 3, the x-intercepts are (-3, 0) and (0, 0) for the first piece.

Set the <u>second piece</u> to zero and solve for x:

\begin{aligned}\implies g(x) & =0\\-\log_4(x-2)+2 & =0\\\log_4(x-2) & =2\end{aligned}

\textsf{Apply log law}: \quad \log_ab=c \iff a^c=b

\begin{aligned}\implies 4^2&=x-2\\x & = 16+2\\x & = 18 \end{aligned}

Therefore, the x-intercept for the second piece is (18, 0).

So the x-intercepts for the piecewise function are (-3, 0), (0, 0) and (18, 0).

<h3><u>Part C</u></h3>

From the graph from part A, and the calculated x-intercepts from part B, the function g(x) is positive between the intervals -3 < x < 0 and 3 ≤ x < 18.

Interval notation:  (-3, 0) ∪ [3, 18)

Learn more about piecewise functions here:

brainly.com/question/11562909

3 0
2 years ago
PLEASE HELP!!
jonny [76]

Answer:

  • A. f(n) = (n + 1)^2 – 1

Step-by-step explanation:

Figure 1

  • 3 = 4 - 1 = 2² - 1 = (1 + 1)² - 1

Figure 2

  • 8 = 9 - 1 = 3² - 1 = (2 + 1)² - 1

Figure 3

  • 15 = 16 - 1 = 4² - 1 = (3 + 1)² - 1

<u>The function is:</u>

  • f(n) = (n + 1)² - 1
7 0
3 years ago
If v varies directly as w, and v=24 when w= 8, find the equation that relates v and w
Zigmanuir [339]

Answer:

v=3w

Step-by-step explanation:

v∝w

v=kw

24=8k

k=24/8 = 3

equation connecting v and w is

v=3w

5 0
3 years ago
In a semiconductor company's quality control test, a machine found that 14 out of a sample of 234 computer chips were defective.
ivann1987 [24]

Answer:

281-282

Step-by-step explanation:

4 0
2 years ago
Carly is a catcher on the school softball team. By the end of the season she had played in 45% of the 40 games the team had play
rewona [7]
22

you need 55% so
55•40 :100
5 0
2 years ago
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