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3 years ago

The absolute value function, f(x) = |x + 2|, is shown.

Mathematics

1 answer:

Georgia [21]3 years ago

5 0

ANSWER

all real numbers

EXPLANATION

The given absolute value function is

$f(x) = |x + 2|$

This function is obtained by shifting the graph of

$y = |x|$

to the left by 2 units.

Since the domain of the parent function is all real numbers, the domain of the transformed function is also all real numbers because the shifting the parent function horizontally or vertically does not affect the domain.

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HELP with these questions

zlopas [31]

Step-by-step explanation:

transform the parent graph of f(x) = ln x into f(x) = - ln (x - 4) by shifting the parent graph 4 units to the right and reflecting over the x-axis

(???, 0): 0 = - ln (x - 4)

$\frac{0}{-1} = \frac{-ln (x - 4)}{-1}$

0 = ln (x - 4)

$e^{0} = e^{ln (x - 4)}$

1 = x - 4

+4 +4

5 = x

(5, 0)

(???, 1): 1 = - ln (x - 4)

$\frac{0}{-1} = \frac{-ln (x - 4)}{-1}$

1 = ln (x - 4)

$e^{1} = e^{ln (x - 4)}$

e = x - 4

+4 +4

e + 4 = x

6.72 = x

(6.72, 1)

Domain: x - 4 > 0

+4 +4

x > 4

(4, ∞)

Vertical asymptotes: there are no vertical asymptotes for the parent function and the transformation did not alter that

No vertical asymptotes

*************************************************************************

transform the parent graph of f(x) = 3ˣ into f(x) = - 3ˣ⁺⁵ by shifting the parent graph 5 units to the left and reflecting over the x-axis

Domain: there is no restriction on x so domain is all real number

(-∞, ∞)

Range: there is a horizontal asymptote for the parent graph of y = 0 with range of y > 0. the transformation is a reflection over the x-axis so the horizontal asymptote is the same (y = 0) but the range changed to y < 0.

(-∞, 0)

Y-intercept is when x = 0:

f(x) = - 3ˣ⁺⁵

= - 3⁰⁺⁵

= - 3⁵

= -243

Horizontal Asymptote: y = 0 (explanation above)

5 0

4 years ago

6n-7=-(8n+7) what is the work and answer

Advocard [28]

6n-7=-8n-7
-7=-14n-7
-14=-14n
1=n

5 0

3 years ago

A regular pentagon has an apothem of 7.3 inches and a perimeter of 53 inches. What is the area of the pentagon? Round your answe

zvonat [6]

Answer:

Area pf the regular pentagon is 193 $inch^{2}$ to the nearest whole number

Step-by-step explanation:

In this question, we are tasked with calculating the area of a regular pentagon, given the apothem and the perimeter

Mathematically, the area of a regular pentagon given the apothem and the perimeter can be calculated using the formula below;

Area of regular pentagon = 1/2 × apothem × perimeter

From the question, we can identify that the value of the apothem is 7.3 inches, while the value of the perimeter is 53 inches

We plug these values into the equation above to get;

Area = 1/2 × 7.3× 53 = 386.9/2 = 193.45 which is 193 $inch^{2}$ to the nearest whole number

3 0

4 years ago

Read 2 more answers

Which of the following is a logical conclusion based on the two statements below? If Jake forgets his snack, then he will be hun

ycow [4]

Answer:

I believe that the answer is either C or D

Step-by-step explanation:

Jake forgot his snack, which could mean that he was hungry at school. But it could be logical to assume that he forgot his breakfast. I may be wrong in both cases, but these are my best guesses!

4 0

3 years ago

What is the value of 6,035

Burka [1]

Answer:

6000

Step-by-step explanation:

because if u round 6,035 it will obviously equal 6,000

8 0

3 years ago

Read 2 more answers