What is the amplitude, period, and phase shift of f(x) = −3 sin(4x − π) − 5?
amplitude = −3; period = 2π; phase shift: x equals pi over four
amplitude = 3; period = pi over two; phase shift: x equals pi over four
amplitude = −3; period = 2π; phase shift: x equals negative pi over four
amplitude = 3; period = pi over two; phase shift: x equals negative pi over four

2nd choice.

Step-by-step explanation:

Let's compare the following:

to

.

They are almost in the same form.

The amplitude is |a|, so it isn't going to be negative.

The period is .

The phase shift is .

If c is positive it has been shifted right c units.

If c is negative it has been shifted left c units.

d is the vertical shift.

If d is negative, it has been moved down d units.

If d is positive, it has been moved up d units.

So we already know two things:

The amplitude is |a|=|-3|=3.

The vertical shift is d=-5 which means it was moved down 5 units from the parent function.

Now let's find the others.

I'm going to factor out 4 from .

Like this:

Now if you compare this to

then b=4 so the period is .

Also in place of c you see which means the phase shift is .

The second choice is what we are looking for.

Second Option

Amplitude = 3; period = pi over two; phase shift: x equals pi over four

Step-by-step explanation:

By definition the sinusoidal function has the following form:

Where

is the Amplitude of the function

is the period of the function

is the phase shift

In this case the function is:

Therefore

include a picture of the drawing in order for me to

step-by-step explanation:

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!