Question

Question 13(Multiple Choice Worth 5 points)

Use the Rational Zeros Theorem to write a list of all potential rational zeros.


f(x) = x3 - 7x2 + 9x - 24


±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24

±1, ±2, ±3, ±4, ±24

±1, ±one divided by two, ±2, ±3, ±4, ±6, ±8, ±12, ±24

±1, ±2, ±3, ±4, ±6, ±12, ±24

Question 14(Multiple Choice Worth 5 points)

Perform the requested operation or operations.


f(x) = 7x + 6, g(x) = 4x2


Find (f + g)(x).


7x + 6 + 4x2

28x3 + 24x

7x + 6 - 4x2

seven x plus six divided by four x squared.

Question 15(Multiple Choice Worth 5 points)

Find a cubic function with the given zeros.


6, -5, 2


f(x) = x3 - 3x2 + 28x + 60

f(x) = x3 - 3x2 - 28x - 60

f(x) = x3 + 3x2 - 28x + 60

f(x) = x3 - 3x2 - 28x + 60

Question 16(Multiple Choice Worth 5 points)

A building has a ramp to its front doors to accommodate the handicapped. If the distance from the building to the end of the ramp is 20 feet and the height from the ground to the front doors is 6 feet, how long is the ramp? (Round to the nearest tenth.)


3.7 ft

5.1 ft

19.1 ft

20.9 ft

Question 17(Multiple Choice Worth 5 points)

Find the domain of the given function.


f(x) = square root of quantity x plus nine divided by quantity x plus three times quantity x minus seven.


x ≥ -9, x ≠ -3, x ≠ 7

x ≠ -9, x ≠ -3, x ≠ 7

All real numbers

x > 0

Question 18(Multiple Choice Worth 5 points)

Find the period of the function.


y = -3 cos x


3

2π

π

pi divided by three


PLEASE HELP ASAP!! 53 points to whoever does

Answer 1

Q13 - A. ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24

Q14 - A.
`7x+6+4x^(2)`

Q15 - D.
`f(x)=x^(3)-3x^(2)-28x+60`

Q16 - D. 20.9 ft

Q17 - A. x ≥ -9, x ≠ -3, x ≠ 7

Q18 - B. 2π

Explanation:

Question 13:

Rational Zeros Theorem states that 'If p(x) is a polynomial with integer coefficients and if
`(p)/(q)` is a zero of p(x) = 0. Then, p is a factor of the constant term of p(x) and q is a factor of the leading coefficient of p(x)'.

Let,
`(p)/(q)` is a zero of
`x^3-7x^2+9x-24=0`. Then, p is a factor of -24 and q is a factor of 1.

Thus, possible values of p = ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24 and q = ±1

This gives, possible values of
`(p)/(q)` are ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24.

Question 14:

We have, f(x) = 7x + 6 and g(x) =
`4x^(2)`

Then, (f+g)(x) = f(x) + g(x) = 7x + 6 +
`4x^(2)`

So, (f+g)(x) =
`7x+6+4x^(2)`

Question 15:

Zeros of the function are given by 6, -5, 2.

Thus, the factored form will be
`(x-6)(x+5)(x-2)=0`

i.e.
`(x^(2)+5x-6x-30)(x-2)=0`

i.e.
`(x^(2)-x-30)(x-2)=0`

i.e.
`(x^(3)-2x^(2)-x^(2)+2x-30x+60=0`

i.e.
`x^(3)-3x^(2)-28x+60=0`

So, the cubic function is
`f(x)=x^(3)-3x^(2)-28x+60`.

Question 16:

Let, the length of the ramp = x feet.

The horizontal length of the ramp = 20 feet

The vertical length of the ramp = 6 feet.

Using Pythagoras Theorem, we have,

`x^(2)=20^(2)+6^(2)`

i.e.
`x^(2)=400+36`

i.e.
`x^(2)=436`

i.e.
`x=\pm 20.9`

Since, the length of the ramp cannot be negative.

Hence, the length of the ramp is 20.9 feet.

Question 17:

We have the function,
`f(x)=(√(x+9))/((x+3)(x-7))`

As the quantities in square roots are always positive, then x+9≥0 i.e. x≥-9.

Also, the function is not defined at x = -3 and x = 7.

Thus, the domain is x ≥ -9 and x ≠ -3, x ≠ 7.

Question 18:

We have the function y = -3 cosx

As, there will be no affect on the period by the quantity -3 and the period of the cosine function is 2π.

Thus, period of y = -3 cosx is 2π.