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Anastaziya [24]
3 years ago
14

Exponential function f(x) has a y intercept of 3 and an x intercept of -2. the function is always increasing as the value of x i

ncreases, but the function never reaches y=4
would it be decreasing or increasing and will it point down or up?
PLZ ANSWER ASAP

Mathematics
1 answer:
Kisachek [45]3 years ago
7 0

Answer:

f(x)=-\left(\dfrac{1}{2}\right)^x+4

The exponential function is increasing and is concave down

Step-by-step explanation:

Let the equation of exponential function be

f(x)=a\cdot b^x+c,\ ,\ b>0

1. Exponential function f(x) has a y intercept of 3, so the graph of f(x) passes through the point (0,3). Thus,

3=a\cdot b^0+c\\ \\3=a+c

2. Exponential function f(x) has an x intercept of -2, so the graph of f(x) passes through the point (-2,0). Thus,

0=a\cdot b^{-2}+c\\ \\0=\dfrac{a}{b^2}+c

3. Function is always increasing as the value of x increases, but the function never reaches y=4, so

c=4

Hence,

\left\{\begin{array}{l}a+4=3\\ \\\dfrac{a}{b^2}+4=0\end{array}\right.\Rightarrow \left\{\begin{array}{l}a=-1\\ \\\dfrac{-1}{b^2}+4=0\end{array}\right.\Rightarrow \left\{\begin{array}{l}a=-1\\ \\b^2=\dfrac{1}{4}\end{array}\right.

So,

a=-1,\\ \\b=\dfrac{1}{2},\\ \\c=4,\\ \\f(x)=-\left(\dfrac{1}{2}\right)^x+4

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9 units^{2} aka 9 units

Step-by-step explanation:

Its pretty simple so what u do is count the sqaures then multiply them and ill do it for you

H=3

B=6

and the formula for a triangle is A=\frac{b*h}{2} so its 3x6/2=9

The answer is 9

5 0
3 years ago
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x2y - 2xy - 24y = y(x2 - 2x - 24) What is the completely factored form of x2y – 2xy – 24y? (xy + 4)(x – 6) xy(x + 4)(x – 6) y(x
likoan [24]

we are given

x^2y-2xy-24y=y(x^2-2x-24)

now, we can factor out right side term

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now, we can plug back

and we get

so,

x^2y-2xy-24y=y(x-6)(x+4).............Answer

5 0
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Anthony Chen's father is going to put a tile border around
Levart [38]

Answer: 12

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One yard is three feet. So three times four is 12 because it makes four yards in total with each side being a yard.

3 0
3 years ago
An angle of measure 120 degrees intersects the unit circle at point (-1/2,√3/2) What is the exact value of cos(120)
notka56 [123]

The exact value of cos120 if the measure 120 degrees intersects the unit circle at point (-1/2,√3/2) is 0.5

<h3>Solving trigonometry identity</h3>

If an angle of measure 120 degrees intersects the unit circle at point (-1/2,√3/2), the measure of cos(120) can be expressed as;

Cos120 = cos(90 + 30)

Using the cosine rule of addition

cos(90 + 30) = cos90cos30 - sin90sin30

cos(90 + 30) = 0(√3/2) - 1(0.5)

cos(90 + 30) = 0 - 0.5

cos(90 + 30) = 0.5

Hence the exact value of cos120 if the measure 120 degrees intersects the unit circle at point (-1/2,√3/2) is 0.5

Learn more on unit circle here: brainly.com/question/23989157

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7 0
2 years ago
If you start with a number, add 5 , then multiply by 7, the result is133. what was the original number?
Natalija [7]
(x+5)*7=133
7x+35=133
7x=98
x=98/7
x=14
5 0
3 years ago
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