On Saturday at 9:00 p.m., the temperature in New York City was -6 degrees Fahrenheit.

Which of these statements is true for f(x)=(1/10)^x

lana66690 [7]

Step-by-step explanation:

Considering the function

$f\left(x\right)=\:\left(\frac{1}{10}\right)^x$

Analyzing option A)

Considering the function

$f\left(x\right)=\:\left(\frac{1}{10}\right)^x$

Putting $x = 1$ in the function

$f\left(1\right)=\:\left(\frac{1}{10}\right)^1$

$f\left(1\right)=\:\left\frac{1}{10}\right$

So, it is TRUE that when $x = 1$ then the out put will be $f\left(1\right)=\:\left\frac{1}{10}\right$

Therefore, the statement that '' The graph contains $\left(1,\:\frac{1}{10}\right)$ '' is TRUE.

Analyzing option B)

Considering the function

$f\left(x\right)=\:\left(\frac{1}{10}\right)^x$

The range of the function is the set of values of the dependent variable for which a function is defined.

$\mathrm{The\:range\:of\:an\:exponential\:function\:of\:the\:form}\:c\cdot \:n^{ax+b}+k\:\mathrm{is}\:\:f\left(x\right)>k$

$k=0$

$f\left(x\right)>0$

Thus,

$\mathrm{Range\:of\:}\left(\frac{1}{10}\right)^x:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)>0\:\\ \:\mathrm{Interval\:Notation:}&\:\left(0,\:\infty \:\right)\end{bmatrix}$

Therefore, the statement that ''The range of $f(x)$ is $y > \frac{1}{10}$ " is FALSE

Analyzing option C)

Considering the function

$f\left(x\right)=\:\left(\frac{1}{10}\right)^x$

The domain of the function is the set of input values which the function is real and defined.

As the function has no undefined points nor domain constraints.

So, the domain is $-\infty \:$

Thus,

$\mathrm{Domain\:of\:}\:\left(\frac{1}{10}\right)^x\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:$

Therefore, the statement that ''The domain of $f(x)$ is $x>0$ '' is FALSE.

Analyzing option D)

Considering the function

$f\left(x\right)=\:\left(\frac{1}{10}\right)^x$

As the base of the exponential function is less then 1.

i.e. 0 < b < 1

Thus, the function is decreasing

Also check the graph of the function below, which shows that the function is decreasing.

Therefore, the statement '' It is always increasing '' is FALSE.

Keywords: function, exponential function, increasing function, decreasing function, domain, range

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3 0

3 years ago

Read 2 more answers

Complete the steps to find the area of the trapezoid.

Yuki888 [10]

Answer:

Area of rectangle: 256

Area of triangle 1: 24

Area of triangle 2: 16

Area of triangle 3: 96

Area of trapezoid: 120

Step-by-step explanation:

I just did the question on the thing so Ik I'm right.

-The graph measures by twos. To get the area of the rectangle get the base times height of it. That would be 16x16=256.

-Get base (8) times height (6) of triangle 1 then divide by 2, remember to count the squares by 2 for finding all areas. The formula would be 1/2(b)(h) because dividing by 2 is the same as multiplying times 1/2. Plug it in and (8)(6)=48 then divide by 2 which equals 24.

-Same formula for triangle 2. Plug it in and (8)(4)=32 and divide by 2 and it equals 16.

-Same formula for triangle 3. Plugged in is (12)(16)=192 divide by 2 and it equals 96.

-To find the area of the trapezoid get your rectangle area (256) and subtract all the triangle areas. So 256 - 6 - 16 - 96 = 120.

4 0

2 years ago

Read 2 more answers

A microgram is equal to 2.3 x 10 grams. How many times greater than a microgram is

vovikov84 [41]

Answer:

yes the aswure is no

Step-by-step explanation:

8 0

2 years ago

When would you use a grouped frequency table over a standard frequency table?

marissa [1.9K]

when a data consists of hundreds of values

hope it helps pls mark me as brainliest

7 0

3 years ago

Elise says, "If you subtract 17 from my number and multiply the difference by negative 6, the result is negative 126." What i

Studentka2010 [4]

Well, I would just reverse it. It seems you just have to reverse the whole problem.

4 0

3 years ago