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3 years ago

What effect does replacing x with x + 2 have on the graph for the function f(x) ?

1 answer:

3 0

The answer is A.

When replacing the variable 'x' by 'x + 2' the graph is shifted 2 units to the left. When we replace the variable, the function changes

from
$f(x) = |x - 3| + 2$

To
$f(x) = |(x + 2) - 3| + 2$
$f(x) = |x - 1| + 2$

And therefore the function is shifted 2 to the left.

You might be interested in

Classify the number -3 into as many categories as it belongs: Natural number, whole number, integer, or rational number.

Effectus [21]

-3 is an integer and a rational number.

Natural numbers and while numbers refer to positive numbers, so -3 cannot be either of those.

3 0

3 years ago

Which is the equation for the line that has a slope of 12 and passes through the point (3, 20)?

sasho [114]

Answer:

y=12x-16

Step-by-step explanation:

y-y1=m(x-x1)

y-20=12(x-3)

y=12x-36+20

y=12x-16

4 0

3 years ago

3,<br> Which expression is equivalent to<br> 56x7y5, if x #0 and y# 0?

spin [16.1K]

Answer:

1960

Step-by-step explanation:

1960

times 56 times 7 time 5 = 1960

6 0

2 years ago

572000 square miles rounded ro the nearest hundred thousand

baherus [9]

It would be rounding it to 600000 because 600000 is the closest 100000x amount where x is an integer. I hope this helped and if I am right could I have brainliest? :)

7 0

3 years ago

You have just opened a new nightclub, Russ' Techno Pitstop, but are unsure of how high to set the cover charge (entrance fee). O

Neko [114]

Answer:

a)q(p)=-15p+ +300

b)R(p)=-15p²+300p

c)C(p)=-30p+1600

d.1)P(p)=-15p²+330p-1600

d.2)p=$11

Step-by-step explanation:

(a).Before getting started, we are going to consider the cartesian plane, where x-axis corresponds to the cover charge and y-axis corresponds to number of guests per night . There, we will locate the following coordinates according to the previous information:

(9,165) (10,150).

Remember that the slope-intercept form of the linear equation is y=mx+b where m is the slope and b is te intercept.

The slope can be calculated by the next formula:

$m=\frac{y2-y1}{x2-x1}$

In this case we will assign (9,165) as the first coordinate and (10,150) as the second one. The order does not matter. At the end we get the same value for m.

Therefore:

$m=\frac{150-165}{10-9} = -15$

Now, we have the slope and two poitns. According to this, and taking into account that point-slope form of the equation of a line is y-y1=m(x-x1), find a linear demand equation.

Any of two coordintates can be selected. In this case we will select the second one.

y-150=-15(x-10) equation 1

Solve equation 1 for y

y=-15x+150+150

y=-15x+300

Above we had defined x as cover charge (p) and y as number of guests (q). Thus, rewrite equation 1.

q(p)=-15p+ +300.

it equation shows the number of guests per night as a function of the cover charge,

(b). The nightly revenue can be calculated multplying the price of the cover charge by the number of guests. So, we just have to multiply the equation 1 by p.

p*q(p)=p*(-15p +300)

R(p)=-15p²+300p equation 2

(c) To get the cost function of the nightclub we just have to multiply the cost of the two non-alcoholic drinks by the number of the guests ( equation 1) and add to it nightly overheads.

C(p)=2*(-15p+300)+1000

C(p)= -30p+600+1000

C(p)=-30p+1600 equation 3

(d) In order to find the profit in terms of the cover charge we will subtract nightly costs ( equation 3) from nightly revenue (equation 2)

P(p)=R(p)-C(p)

P(p)=-15p²+300p - (-30p+1600)

P(p)=-15p²+300p+30p-1600

P(p)=-15p²+330p-1600

To determine that the entrance fee we should charge for a maximum profit we are going to use the first derivative test (y'(x)=0) in order to find an extremum point.

Compute the first derivative of P(p)

P'(p)=-30p+330=0

30p=330

p=330/30

p= $11

The entrance fee that we should charge for a maximum profit is p=$11 per guest.

5 0

3 years ago