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3 years ago

Let g(x) be the reflection of f(x) = x 2 + 3 in the x-axis. What is the function rule for g(x)?

2 answers:

3 0

G(x) will be g(x)=-2x-3 because it is a reflection of f(x) over the x-axis. F(x)'s reflection over the x-axis will become -f(x).

taurus [48]3 years ago

3 0

Answer:

$g(x)=-x^2-3$

Step-by-step explanation:

The parent function is $x^2+3$

Now, the function g(x) is obtained by reflecting the graph of f(x) about the x-axis.

When the parent function f(x) is reflected about the x-axis then the translated function is -f(x)

Therefore, we have g(x)=-f(x)

Hence, the equation of g(x) is

$g(x)=-f(x)\\\\g(x)=-(x^2+3)\\\\g(x)=-x^2-3$

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Lim x->pi/3 ((2cosx-1)/(tan^2x-3))

beks73 [17]

You can check that the limit comes in an undefined form:

$\displaystyle \lim_{x\to\frac{\pi}{3}} \frac{2\cos(x)-1}{\tan^2(x)-3}=\dfrac{0}{0}$

In these cases, we can use de l'Hospital rule, and evaluate the limit of the ratio of the derivatives. We have:

$\dfrac{\text{d}}{\text{d}x}2\cos(x)-1 = -2\sin(x)$

and

$\dfrac{\text{d}}{\text{d}x}\tan^2(x)-3 = 2\dfrac{\tan(x)}{\cos^2(x)}=\dfrac{2\sin(x)}{\cos^3(x)}$

So, we have

$\displaystyle \lim_{x\to\frac{\pi}{3}} \frac{2\cos(x)-1}{\tan^2(x)-3}=\lim_{x\to\frac{\pi}{3}} \dfrac{-2\sin(x)}{\frac{2\sin(x)}{\cos^3(x)}}=\lim_{x\to\frac{\pi}{3}}-\cos^3(x)=-\cos^3\left(\dfrac{\pi}{3}\right)$

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3 years ago

determine the event space for rolling a sum of 12 with two dice. how many elements are in the event space?

WARRIOR [948]

Answer: 1

Step-by-step explanation:

Only one element is in the event space for rolling the sum of 12 with two dice

(6,6)

If you must roll the sum of 12 with two dice, you must have rolled 6 in the two dice

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3 years ago

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solmaris [256]

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3 years ago

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Yesterday the Bandits scored 56 points in their basketball game. Today they scored 42 points. What is the percent decrease of Th

FromTheMoon [43]

Answer:

x = 25% percent decrease

Step-by-step explanation:

For this problem we will use percentage calculation and make proportion:

Initial value 56 points is worth 100%

Second value 56 - 42 = 14 points of decrease is worth x%

56 : 14 = 100 : x

When we multiply external and internal members we get:

56 · x = 14 · 100 => x = 1400/56 = 25%

x = 25% percent decrease

God with you!!!

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3 years ago