MATH SOLVE

3 months ago

Q:
# 1. Find the domain of the given function. (1 point)f(x) = square root of quantity x plus three divided by quantity x plus eight times quantity x minus two.A) x > 0B) All real numbersC) x ≥ -3, x ≠ 2D) x ≠ -8, x ≠ -3, x ≠ 22. Identify intervals on which the function is increasing, decreasing, or constant.g(x) = 2 - (x - 7)2 (1 point)A) Increasing: x < 2; decreasing: x > 2B) Increasing: x < -7; decreasing: x > -7C) Increasing: x < 7; decreasing: x > 7D)Increasing: x > 2; decreasing: x < 23. Perform the requested operation or operations.f(x) = 4x + 7, g(x) = 3x2Find (f + g)(x). (1 point)A) four x plus seven divided by three x squared.B) 12x3 + 21xC) 4x + 7 + 3x2D) 4x + 7 - 3x24. Perform the requested operation or operations.f(x) = x minus five divided by eight. ; g(x) = 8x + 5, find g(f(x)). (1 point)A) g(f(x)) = x - five divided by eight.B) g(f(x)) = xC) g(f(x)) = 8x + 35D) g(f(x)) = x + 105. Find f(x) and g(x) so that the function can be described as y = f(g(x)).y = nine divided by square root of quantity five x plus five. (1 point)A) f(x) = nine divided by square root of x. , g(x) = 5x + 5B) f(x) = square root of quantity five x plus five. , g(x) = 9C) f(x) = nine divided by x. , g(x) = 5x + 5D) f(x) = 9, g(x) = square root of quantity x plus five6. A satellite camera takes a rectangular-shaped picture. The smallest region that can be photographed is a 4-km by 4-km rectangle. As the camera zooms out, the length l and width w of the rectangle increase at a rate of 3 km/sec. How long does it take for the area A to be at least 4 times its original size? (1 point)A) 4.94 secB) 3.28 secC) 9.7 secD) 1.33 sec7. Find the inverse of the function. (1 point)f(x) = the cube root of quantity x divided by seven. - 9A) f-1(x) = 21(x + 9)B) f-1(x) = [7(x + 9)]3C) f-1(x) = 7(x3 + 9)D) f-1(x) = 7(x + 9)38. Describe how the graph of y= x2 can be transformed to the graph of the given equation.y = (x - 14)2 - 9 (1 point)A) Shift the graph of y = x2 right 14 units and then up 9 units.B) Shift the graph of y = x2 down 14 units and then left 9 units.C) Shift the graph of y = x2 right 14 units and then down 9 unitsD) Shift the graph of y = x2 left 14 units and then down 9 units9. Describe how to transform the graph of f into the graph of g. f(x) = alt='square root of quantity x minus nine.' and g(x) = alt='square root of quantity x plus five. 'A) Shift the graph of f right 14 units.B) Shift the graph of f right 4 units.C) Shift the graph of f left 14 units.D) Shift the graph of f left 4 units.10. If the following is a polynomial function, then state its degree and leading coefficient. If it is not, then state this fact.f(x) = -16x5 - 7x4 - 6 (1 point)A) Degree: -16; leading coefficient: 5B) Degree: 5; leading coefficient: -16C) Not a polynomial function.D) Degree: 9; leading coefficient: -1611. Write the quadratic function in vertex form.y = x2 + 4x + 7 (1 point)A) y = (x + 2)2+ 3B) y = (x + 2)2 - 3C) y = (x - 2)2 - 3D) y = (x - 2)2 + 312. Find the zeros of the function.f(x) = 3x3 - 12x2 - 15x (1 point)A) 0, 1, and -5B) -1 and 5C) 0, -1, and 5D) 1 and -513. Find a cubic function with the given zeros.7, -3, 2 (1 point)A) f(x) = x3 - 6x2 - 13x - 42B) f(x) = x3 - 6x2 + 13x + 42C) f(x) = x3 - 6x2 - 13x + 42D) f(x) = x3 + 6x2 - 13x + 4214. Find the remainder when f(x) is divided by (x - k).f(x) = 7x4 + 12x3 + 6x2 - 5x + 16; k = 3 (1 point)A) 188B) 946C) 1,704D) 2,51215. Use the Rational Zeros Theorem to write a list of all potential rational zeros.f(x) = x3 - 10x2 + 4x - 24 (1 point)A) ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24B) ±1, ±2, ±3, ±4, ±24C) ±1, ± alt='one divided by two', ±2, ±3, ±4, ±6, ±8, ±12, ±24D) ±1, ±2, ±3, ±4, ±6, ±12, ±24PLEASE NEED HELP HERE ASAP PRIORITY HELP WOULD BE APPRECIATED

Accepted Solution

A:

1) Find the domain of the given function. f(x) = square root of quantity x plus three divided by quantity x plus eight times quantity x minus two.

using a graphical tool see the attachment

the answer is C) x ≥ -3, x ≠ 2

2. Identify intervals on which the function is increasing, decreasing, or constant.

g(x) = 2 - (x - 7)2

using a graphical tool

see the attachment

the answer is C) Increasing: x < 7; decreasing: x > 7

3. Perform the requested operation or operations.

f(x) = 4x + 7, g(x) = 3x2

Find (f + g)(x).

(f + g)(x) = f(x) + g(x)

(f + g)(x) = 4x + 7 + 3x^2

(f + g)(x) = 3x^2 + 4x + 7

The answer is C) 4x + 7 + 3x2

4. Perform the requested operation or operations.

f(x) = x minus five divided by eight. ; g(x) = 8x + 5, find g(f(x)).

f(x)=(x-5)/8 g(x)=8x+5

g(f(x))=8((x-5)/8)+5=x-5+5=x

the answer is B) g(f(x)) = x

5. Find f(x) and g(x) so that the function can be described as y = f(g(x)).y = nine divided by square root of quantity five x plus five.

y=f(g(x))=9/((5x+5) ^1/2)

let do

g(x)=5x+5...........so

f(x)= 9/( x^1/2)

the answer is A) f(x) = nine divided by square root of x. , g(x) = 5x + 5

6. A satellite camera takes a rectangular-shaped picture. The smallest region that can be photographed is a 4-km by 4-km rectangle. As the camera zooms out, the length l and width w of the rectangle increase at a rate of 3 km/sec. How long does it take for the area A to be at least 4 times its original size?

Original size- >4km*4km=16 km2

4 times its original size---------------4*(16km2)-----64 Km2----------- > 8 km by 8 Km

Therefore

3km----------------------------- 1 sec

(8km-4km)---------------------x

X=4/3=1.33 sec

The answer is D) 1.33 sec

7. Find the inverse of the function.

f(x) = the cube root of quantity x divided by seven. - 9

to solve, replace f(x) with y , switch x and y, solve for y and replace y with f⁻¹(x)

f(x)=((x/7)-9) ^(1/3)

replace f(x) with y

y=((x/7)-9) ^(1/3)

switch x and y

x=((y/7)-9) ^(1/3)

solve for y

x^3=((y/7)-9)

x^3+9=y/7

y=7(x^3+9)

the answer is C) f-1(x) = 7(x3 + 9)

8. Describe how the graph of y= x2 can be transformed to the graph of the given equation.y = (x - 14)2 – 9

using a graphical tool see the attachment the answer is C) Shift the graph of y = x2 right 14 units and then down 9 units

9. Describe how to transform the graph of f into the graph of g. f(x) = alt='square root of quantity x minus nine.' and g(x) = alt='square root of quantity x plus five. '

f(x)=(x-9) ^1/2 g(x)=(x+5) ^1/2

using a graphical tool see the attachment

the answer is C) Shift the graph of f left 14 units

10. If the following is a polynomial function, then state its degree and leading coefficient. If it is not, then state this fact.

f(x) = -16x5 - 7x4 – 6

The answer is B) Degree: 5; leading coefficient: -16

11. Write the quadratic function in vertex form.y = x2 + 4x + 7

Complete the square on the right side of the equation

Use the form ax2+bx+cax2+bx+c, to find the values of a, b, and c.

a=1,b=4,c=7

Consider the vertex form of a parabola.

a(x+d)2+e

Find the value of dd using the formula d=b/2a

d=4/(2*1)=2

Find the value of e using the formula e=c−b2/4a

e=7−4=3

Substitute the values of a, d, and e into the vertex form a(x+d)2+e

(x+2)2+3

The answer is A) y = (x + 2)2+ 3

12. Find the zeros of the function.

f(x) = 3x3 - 12x2 - 15x

using a graphical tool (see the attachment)x1=-1

x2=0

x3=5

The answer is C) 0, -1, and 5

13. Find a cubic function with the given zeros.7, -3, 2

X1=7

X2=-3

X3=2

f(x)=(x-7)(x+3)(x-2)=(x2-4x-21)(x-2)=x3-6x2-13x+42

the answer is C) f(x) = x3 - 6x2 - 13x + 42

14. Find the remainder when f(x) is divided by (x - k).f(x) = 7x4 + 12x3 + 6x2 - 5x + 16; k = 3

f(x)=7(3)4+12(3)3+6(3)2-5(3)+16=946

The answer is the B) 94615. Use the Rational Zeros Theorem to write a list of all potential rational zerosf(x) = x3 - 10x2 + 4x - 24The constant term of () is -24 The leading coefficient is 1. We have to only consider the factors of the constant (leading coefficient = 1) The factors are 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 8, -8, 12, -12, 24, -24 The answer is A) ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24

using a graphical tool see the attachment

the answer is C) x ≥ -3, x ≠ 2

2. Identify intervals on which the function is increasing, decreasing, or constant.

g(x) = 2 - (x - 7)2

using a graphical tool

see the attachment

the answer is C) Increasing: x < 7; decreasing: x > 7

3. Perform the requested operation or operations.

f(x) = 4x + 7, g(x) = 3x2

Find (f + g)(x).

(f + g)(x) = f(x) + g(x)

(f + g)(x) = 4x + 7 + 3x^2

(f + g)(x) = 3x^2 + 4x + 7

The answer is C) 4x + 7 + 3x2

4. Perform the requested operation or operations.

f(x) = x minus five divided by eight. ; g(x) = 8x + 5, find g(f(x)).

f(x)=(x-5)/8 g(x)=8x+5

g(f(x))=8((x-5)/8)+5=x-5+5=x

the answer is B) g(f(x)) = x

5. Find f(x) and g(x) so that the function can be described as y = f(g(x)).y = nine divided by square root of quantity five x plus five.

y=f(g(x))=9/((5x+5) ^1/2)

let do

g(x)=5x+5...........so

f(x)= 9/( x^1/2)

the answer is A) f(x) = nine divided by square root of x. , g(x) = 5x + 5

6. A satellite camera takes a rectangular-shaped picture. The smallest region that can be photographed is a 4-km by 4-km rectangle. As the camera zooms out, the length l and width w of the rectangle increase at a rate of 3 km/sec. How long does it take for the area A to be at least 4 times its original size?

Original size- >4km*4km=16 km2

4 times its original size---------------4*(16km2)-----64 Km2----------- > 8 km by 8 Km

Therefore

3km----------------------------- 1 sec

(8km-4km)---------------------x

X=4/3=1.33 sec

The answer is D) 1.33 sec

7. Find the inverse of the function.

f(x) = the cube root of quantity x divided by seven. - 9

to solve, replace f(x) with y , switch x and y, solve for y and replace y with f⁻¹(x)

f(x)=((x/7)-9) ^(1/3)

replace f(x) with y

y=((x/7)-9) ^(1/3)

switch x and y

x=((y/7)-9) ^(1/3)

solve for y

x^3=((y/7)-9)

x^3+9=y/7

y=7(x^3+9)

the answer is C) f-1(x) = 7(x3 + 9)

8. Describe how the graph of y= x2 can be transformed to the graph of the given equation.y = (x - 14)2 – 9

using a graphical tool see the attachment the answer is C) Shift the graph of y = x2 right 14 units and then down 9 units

9. Describe how to transform the graph of f into the graph of g. f(x) = alt='square root of quantity x minus nine.' and g(x) = alt='square root of quantity x plus five. '

f(x)=(x-9) ^1/2 g(x)=(x+5) ^1/2

using a graphical tool see the attachment

the answer is C) Shift the graph of f left 14 units

10. If the following is a polynomial function, then state its degree and leading coefficient. If it is not, then state this fact.

f(x) = -16x5 - 7x4 – 6

The answer is B) Degree: 5; leading coefficient: -16

11. Write the quadratic function in vertex form.y = x2 + 4x + 7

Complete the square on the right side of the equation

Use the form ax2+bx+cax2+bx+c, to find the values of a, b, and c.

a=1,b=4,c=7

Consider the vertex form of a parabola.

a(x+d)2+e

Find the value of dd using the formula d=b/2a

d=4/(2*1)=2

Find the value of e using the formula e=c−b2/4a

e=7−4=3

Substitute the values of a, d, and e into the vertex form a(x+d)2+e

(x+2)2+3

The answer is A) y = (x + 2)2+ 3

12. Find the zeros of the function.

f(x) = 3x3 - 12x2 - 15x

using a graphical tool (see the attachment)x1=-1

x2=0

x3=5

The answer is C) 0, -1, and 5

13. Find a cubic function with the given zeros.7, -3, 2

X1=7

X2=-3

X3=2

f(x)=(x-7)(x+3)(x-2)=(x2-4x-21)(x-2)=x3-6x2-13x+42

the answer is C) f(x) = x3 - 6x2 - 13x + 42

14. Find the remainder when f(x) is divided by (x - k).f(x) = 7x4 + 12x3 + 6x2 - 5x + 16; k = 3

f(x)=7(3)4+12(3)3+6(3)2-5(3)+16=946

The answer is the B) 94615. Use the Rational Zeros Theorem to write a list of all potential rational zerosf(x) = x3 - 10x2 + 4x - 24The constant term of () is -24 The leading coefficient is 1. We have to only consider the factors of the constant (leading coefficient = 1) The factors are 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 8, -8, 12, -12, 24, -24 The answer is A) ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24