All categories

1 year ago

Instructions: For the function given, determine the direction and amount of vertical shift from the function =(2).

Mathematics

2 answers:

posledela1 year ago

5 0

SOLUTION

From the translation given, the amount of vertical shift is 3 units down

This was derived from -3

Hence the answer is 3 units down

Lemur [1.5K]1 year ago

4 0

The function is translated 1 unit to the left, 3 units down, and is stretched by a factor of 6.

Translated functions use their principle (original) function and add lateral and vertical changes to the function. The principle function is y=(2)^x. Therefore, adding one to that x-value would shift it to the left by 1 unit for every x-value. NOTE: +1 is actually to the right, but transformations reverse that, so it is actually to the left towards the negative domains. The entire function is shifted down 3 units; the “-3” as the last term is subtracting the entire function, so the y-coordinates will all shift down 3 units. And the “a” value of the function is 6. When a>0, the function stretches. So, the function will stretch by a factor of 6, since it is multiplying the entire range of the function.

You might be interested in

Can anybody help plzz?? 65 points

Yakvenalex [24]

Answer:

$\frac{dy}{dx} =\frac{-8}{x^2} +2$

$\frac{d^2y}{dx^2} =\frac{16}{x^3}$

Stationary Points: See below.

General Formulas and Concepts:

Pre-Algebra

Equality Properties

Calculus

Derivative Notation dy/dx

Derivative of a Constant equals 0.

Stationary Points are where the derivative is equal to 0.

1st Derivative Test - Tells us if the function f(x) has relative max or mins. Critical Numbers occur when f'(x) = 0 or f'(x) = undef
2nd Derivative Test - Tells us the function f(x)'s concavity behavior. Possible Points of Inflection/Points of Inflection occur when f"(x) = 0 or f"(x) = undef

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Quotient Rule: $\frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}$

Step-by-step explanation:

Step 1: Define

$f(x)=\frac{8}{x} +2x$

Step 2: Find 1st Derivative (dy/dx)

Quotient Rule [Basic Power]: $f'(x)=\frac{0(x)-1(8)}{x^2} +2x$
Simplify: $f'(x)=\frac{-8}{x^2} +2x$
Basic Power Rule: $f'(x)=\frac{-8}{x^2} +1 \cdot 2x^{1-1}$
Simplify: $f'(x)=\frac{-8}{x^2} +2$

Step 3: 1st Derivative Test

Set 1st Derivative equal to 0: $0=\frac{-8}{x^2} +2$
Subtract 2 on both sides: $-2=\frac{-8}{x^2}$
Multiply x² on both sides: $-2x^2=-8$
Divide -2 on both sides: $x^2=4$
Square root both sides: $x= \pm 2$

Our Critical Points (stationary points for rel max/min) are -2 and 2.

Step 4: Find 2nd Derivative (d²y/dx²)

Define: $f'(x)=\frac{-8}{x^2} +2$
Quotient Rule [Basic Power]: $f''(x)=\frac{0(x^2)-2x(-8)}{(x^2)^2} +2$
Simplify: $f''(x)=\frac{16}{x^3} +2$
Basic Power Rule: $f''(x)=\frac{16}{x^3}$

Step 5: 2nd Derivative Test

Set 2nd Derivative equal to 0: $0=\frac{16}{x^3}$
Solve for x: $x = 0$

Our Possible Point of Inflection (stationary points for concavity) is 0.

Step 6: Find coordinates

Plug in the C.N and P.P.I into f(x) to find coordinate points.

x = -2

Substitute: $f(-2)=\frac{8}{-2} +2(-2)$
Divide/Multiply: $f(-2)=-4-4$
Subtract: $f(-2)=-8$

x = 2

Substitute: $f(2)=\frac{8}{2} +2(2)$
Divide/Multiply: $f(2)=4 +4$
Add: $f(2)=8$

x = 0

Substitute: $f(0)=\frac{8}{0} +2(0)$
Evaluate: $f(0)=\text{unde} \text{fined}$

Step 7: Identify Behavior

See Attachment.

Point (-2, -8) is a relative max because f'(x) changes signs from + to -.

Point (2, 8) is a relative min because f'(x) changes signs from - to +.

When x = 0, there is a concavity change because f"(x) changes signs from - to +.

3 0

3 years ago

What is 4^6 . 4^6 please help

KonstantinChe [14]

Answer:

4^12 or 16777216

Step-by-step explanation:

4^6* 4^6

We can symplify 4^6* 4^6

Since they both have the same base, we can add there exponent:

4^6* 4^6= 4^12

4^12 equals to 16777216

8 0

3 years ago

The quotient of a and b

S_A_V [24]

Answer: take the first digit of a and divide it by b

Step-by-step explanation: and that should give you your answer and if not please feel free to mesage me.

8 0

2 years ago

What is the surface of a triangular prism 1 cm 1 cm 1.2 cm 1.2 cm 0.8 cm

Masja [62]

Answer:

dddddddd

Step-by-step explanation:

ddddddd

5 0

3 years ago

A hot air balloon can hold u to 300 pounds of weight the balloons pilot weighs 140 pounds how many 20 pound bags of sand b can h

Mashcka [7]

You can have 8, 20lb bags of sand plus the balloon pilot

3 0

3 years ago