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Darya [45]
2 years ago
12

Describe the domain and range of y=2(3)^x-2+5

Mathematics
2 answers:
evablogger [386]2 years ago
8 0

Answer:

the domain is "the set of all real numbers."

the range of the given function is (5, infinity)

Step-by-step explanation:

This is an exponential function.  For the sake of clarity you must enclose "x - 2" inside parentheses:  f(x) = 2(3)^(x-2).  This function is defined for all real x-values, so the domain is "the set of all real numbers."  

Focusing on  (3)^x:  This has the same shape as the basic exponential y = e^x; the graph starts in Quadrant II and increases with x, more and more rapidly as you pass x = 0.  The functions y = e^x and that of y = 3^x are always positive.  Likewise in the case of f(x) = 2(3)^(x-2):  the function is always positive.  If we look at f(x) = 2(3)^(x-2) alone, we conclude that the domain is (0, infinity).  But that " + 5 " in y=2(3)^(x-2) + 5 translates the entire graph of f(x) = 2(3)^(x-2) upward by 5 units.

Thus, the range of the given function is (5, infinity).

allochka39001 [22]2 years ago
5 0

Answer:

Step-by-step explanation:

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Simplify the following expression.
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Answer:

i dont know what you mean but

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3 years ago
Brittany will be working full time this summer to save for her goal of having 10,000 by the time she is 21. Brittany has an acco
photoshop1234 [79]

Answer:

$ 8,695.35

Step-by-step explanation:

This is a compound interest question

Amount after t years = A = P(1 + r/n)^nt

Where P = Initial Amount saved

r = interest rate

t = time in years

n = compounding frequency

A = 10,000

r = 3.5 %

t = 21 - 17 = 4 years

n = Compounded monthly = 12

Step 1

Converting R percent to r a decimal

r = R/100 = 3.5%/100 = 0.035 per year.

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

Solving our equation:

P = 10000 / ( 1 + (0.035/12)^12 ×4 =

P = $8,695.35

The principal investment required to get a total amount, principal plus interest, of $10,000.00 from interest compounded monthly at a rate of 3.5% per year for 4 years is $8,695.35.

8 0
2 years ago
School lunch costs $1.25 per day. If there are 21 school days
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$26.25

Step-by-step explanation:

1.25 per day

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2 years ago
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The figure below is a square pyramid where the height of the pyramid is 2 centimeters and the volume is 24 cubic centimeters. If
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Step-by-step explanation:

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2 years ago
Create the f(x) function based on the table. Your answer should be in function notation. X f(x) - 10 -6 -9 -5 1-8 -4 -7 1-3 5 9​
Minchanka [31]

Answer:

f(x) = x + 4

Step-by-step explanation:

First create an equation in slope-intercept form, y = mx + b. To do this, find the rate of change or slope (m), and the y-intercept (b).

Using two pairs, (-7, -3) and (-8, -4),

slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-4 -(-3)}{-8 -(-7)} = \frac{-1}{-1} = 1

m = 1

To find b, substitute m = 1, x = -7 and y = -3 into y = mx + b.

Thus:

-3 = (1)(-7) + b

-3 = -7 + b

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4 = b

b = 4.

Replace y with f(x), m with 1 and b with 4 in y = mx + b.

The function would be:

f(x) = x + 4

6 0
3 years ago
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