Evaluate ƒ(x) = –4x – 5 for x =

HELP PLEASE!!!!!!!!!!!

emmainna [20.7K]

Answer:

Part 1) $y=-x^{2}$ ---> Translated up by 1 units

Part 2) $y=x^{2}+1$ ---> Reflected across the x-axis

Part 3) $y=-(x+1)^{2}-1$ ---> Translated left by 1 unit

Part 4) $y=-(x-1)^{2}-1$ ----> Translated right by 1 unit

Part 5) $y=-x^{2}-1$ ----> Reflected across the y-axis

Part 6) $y=-x^{2}-2$ ----> Translated down by 1 unit

Step-by-step explanation:

we know that

The parent function is

$y=-x^{2}-1$ ----> this is a vertical parabola open downward with vertex at (0,-1)

Calculate each case

Part 1) Translated up by 1 unit

The rule of the translation is

(x,y) -----> (x,y+1)

so

(0,-1) ----> (0,-1+1)

(0,1) ----> (0,0) ----> the new vertex

The new function is equal to

$y=-x^{2}$

Part 2) Reflected across the x-axis

The rule of the reflection is

(x,y) -----> (x,-y)

so

(0,-1) ----> (0,1) ----> the new vertex

The new function is equal to

$y=x^{2}+1$

Part 3) Translated left by 1 unit

The rule of the translation is

(x,y) -----> (x-1,y)

so

(0,-1) ----> (0-1,-1)

(0,1) ----> (-1,-1) ----> the new vertex

The new function is equal to

$y=-(x+1)^{2}-1$

Part 4) Translated right by 1 unit

The rule of the translation is

(x,y) -----> (x+1,y)

so

(0,-1) ----> (0+1,-1)

(0,1) ----> (1,-1) ----> the new vertex

The new function is equal to

$y=-(x-1)^{2}-1$

Part 5) Reflected across the y-axis

The rule of the reflection is

(x,y) -----> (-x,y)

so

(0,-1) ----> (0,-1) ----> the new vertex

The new function is equal to

$y=-x^{2}-1$

Part 6) Translated down by 1 unit

The rule of the translation is

(x,y) -----> (x,y-1)

so

(0,-1) ----> (0,-1-1)

(0,1) ----> (0,-2) ----> the new vertex

The new function is equal to

$y=-x^{2}-2$

3 0

3 years ago

Madeline received $300 for her birthday. She deposits it into a savings account with an interest rate of 2.45%. She makes monthl

oee [108]

Answer:

b. $1,587.57

Step-by-step explanation:

A financial calculator will tell you the value of Madeline's account after 8 years will be $16,287.57. In that time, she will have deposited ...

$300 +96×150 = $14,700

The interest earned is the difference between her account balance and the amount she deposited:

$16,287.57 -14,700 = $1,587.57 . . . interest earned

_____

Account value calculation

The future value of the initial $300 deposit after 8 years is ...

A = P(1 +r/n)^(nt)

for principal P earning annual rate r compounded n times per year for t years.

A = $300(1 +0.0245/12)^(12·8) ≈ $364.89

The future value of the sum of $150 deposits monthly (at the beginning of the month) will be ...

A = $150((1+r/n)^(nt) -1)(1 +n/r) = $15,922.68

So, the total value of Madeline's account in 8 years is ...

$364.89 +15,922.68 = $16,287.57

_____

Comment on account value

In problems of this nature, it is always necessary to determine when the deposits are made relative to when the account value is measured. Here, we assume the $300 deposit is immediate, and its value is measured 8 years hence.

The monthly deposits are not described in that detail. In order to get any of the numbers in the answer list, we need to assume the deposits are at the beginning of the month. If we assume they are at the end of the month, the amount of interest is reduced by about $33.18, the last month's interest.

7 0

3 years ago

What is the quotient of 1,078 and 14

pantera1 [17]

Answer:

77 is the quotient of 1,078 and 14.

Step-by-step explanation:

quotient is the answer to a division problem.

numerator/denominator = quotient

1,078/14 = quotient

1,078/14 = 77

Have a nice day!

3 0

3 years ago

Harry is at the store buying cheese. The cost of the cheese

DaniilM [7]

Answer: $2

Step-by-step explanation: for each 4 ounces. it is a dollar. and since Harry got 8 ounces, it would be $2

7 0

2 years ago

an electrician charges $50 to make a house call and $40 for each hour worked. if you have $200 can you afford a repair that take

mariarad [96]

No. you will be short 10$ so it will not work.

7 0

3 years ago

Read 2 more answers

Evaluate ƒ(x) = –4x – 5 for x = –1.