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Iteru [2.4K]
3 years ago
6

Analyze a graph In Exercise,analyze and sketch the graph of the function.Label any relative extrema, points of inflation,and asy

mptotes.
f(x) = e^x - e^-x/2

Mathematics
1 answer:
ZanzabumX [31]3 years ago
8 0

Answer:

Step-by-step explanation:

Given is a function f(x)

f(x) = e^x -e^{-\frac{{x}}{2}

We have to analyse and sketch the graph

X intercept : Put y =0, we get x=0

Y intercept: Put x =0 , we get y =0

No exception for x or y and hence set of all real numbers is domain and range.

f'(x) = (e^x +1/2 e^{-\frac{{x}}{2})

f' becomes 0 not at finite points

So relative extreme

Graph is sketched and attached

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How do you rewrite equations in slope intercept form ?
PIT_PIT [208]
Slope intercept form is y = mx+b, so you can see that you set the equation equal to y. So if the equation is 2y+3x=6, then you solve for y to put it in slope intercept form.
2y + 3x = 6
2y = -3x + 6
y = (-3/2)x + 3

Keep in mind that the term with the x has to be before the constant, so it can't be y = 3 -(3/2)x

And by the way m is the slope and b is y-intercept, so in <span>y = (-3/2)x + 3, -3/2 is slope and (0,3) is y-intercept</span>
3 0
3 years ago
Please help me thank you.
Alona [7]

Answer:

\large\boxed{1.\ (4)^{-3x^2}=\left(\dfrac{1}{4}\right)^{3x^2}}

\large\boxed{2.\ ab^{-3x}=a\left(\dfrac{1}{b}\right)^{3x}=a\left[\left(\dfrac{1}{b}\right)^3\right]^x}

Step-by-step explanation:

Use:\ a^{-n}=\left(\dfrac{1}{a}\right)^n\\------------\\\\(4)^{-3x^2}=\left[(4)^{-1}\right]^{3x^2}=\left(\dfrac{1}{4}\right)^{3x^2}

Use:\ a^{-n}=\left(\dfrac{1}{a}\right)^n\ and\ (a^n)^m=a^{nm}\\--------------------\\\\ab^{-3x}=a\cdot b^{-3x}=a\left[(b)^{-1}\right]^{3x}=a\left(\dfrac{1}{b}\right)^{3x}\\\\ab^{-3x}=a\left(\dfrac{1}{b}\right)^{3x}=a\left[\left(\dfrac{1}{b}\right)^3\right]^x

8 0
2 years ago
The longer leg of a right triangle is 4cm longer than the shorter leg. the hypotenuse is 8cm longer than the shorter leg. find t
Alexeev081 [22]
Longer leg = x + 4

Shorter leg = x

Hypotenuse = x + 8


Using Pythagorean Theorem:

a^2 + b^2 = c^2

(x + 4)^2 + x^2 = (x + 8)^2

x^2 + 8x + 16 + x^2 = x^2 + 16x + 64

2x^2 + 8x + 16 = x^2 + 16x + 64

2x^2 +8x = x^2 + 16x + 48

2x^2 - 8x = x^2 + 48

x^2 - 8x = 48

x^2 - 8x - 48 = 0

You can complete the square from here or use the quadratic formula.

Completing the square:

x^2 - 8x = 48

x^2 - 8x + (-8/2)^2 = 48 + (-8/2)^2

x^2 - 8x + 16 = 48 + 16

(x - 4)(x - 4) = 64 or (x - 4)^2 = 64

x - 4 = +√64 OR x - 4 = -√64

x - 4 = +8 OR x - 4 = -8

x = 12 OR x = -4

However, you can't use negative 4 as a length because your length needs to be a positive.

So x will be 12.


Shorter leg: 12

Longer leg: 12 + 4

Hypotenuse: 12 + 8

8 0
3 years ago
What is the difference of 7 1/6−3 5/8? fractions. with common denominators
lord [1]

Answer: 3 13/24

Step-by-step explanation:

<u>Turn 7 1/6 into an Improper Fraction:</u>

43/6 - 3 5/8

<u>Turn 3 5/8 into an Improper Fraction:</u>

43/6 - 29/8

<u>Subtract:</u>

43/6 - 29/8= 85/24

<u>Turn 85/24 into a Mixed Number (Final Step):</u>

85/24 = 3 13/24

<u>Answer:</u>

3 13/24

Hope this Helps!

<u></u>

4 0
3 years ago
Find equation of the line passing through(0,-3),which has a gradient of 2
WINSTONCH [101]

Answer:

y = 2x - 3

Step-by-step explanation:

y - - 3 = 2(x-0)

y + 3 = 2x

y = 2x -3

7 0
2 years ago
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