The line starts at (2,4) and then chose The best point of the following for it to pass through; (6,1) (10,1) (10,3)

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

6 1/2 how many inches

sveticcg [70]

Answer:

78 inches

Step-by-step explanation:

12 TIMES 6 = 72

72+6=78

6 0

3 years ago

Given the following linear function sketch the graph of the function and find the domain and range f(x)=-3x+7

natka813 [3]

<h3>Answer:</h3>

see attached for a graph

domain and range: all real numbers

<h3>Step-by-step explanation:</h3>

The function is written in slope-intercept form, showing that it has a slope of -3 and a y-intercept of +7. The y-intercept (0, 7) is a point on the line, as is a point 1 unit to the right and down 3 units, (1, 4).

The graph will be the line through these two points.

_____

As with any odd-degree polynomial function, both domain and range are all real numbers: (-∞, ∞).

6 0

3 years ago

If the mean is 298 and standard deviation is 22 what is the probability that a random sample of 42 pregnancies has a mean gestat

anyanavicka [17]

Answer:

The probability is 0.9909.

Step-by-step explanation:

Test statistic (z) = (sample mean - population mean) ÷ (sd/√n)

sample mean = 290 days

population mean = 298 days

sd = 22 days

n = 42

z = (290 - 298) ÷ (22/√42) = -8 ÷ 3.395 = -2.36

The cumulative area of the test statistic is the probability that the mean gestation period is less than 290 days. The cumulative area is 0.9909. Therefore the probability is 0.9909.

7 0

3 years ago

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Find the missing measures for the rectangle<br> l = _?_<br> w = 4.2 m<br> A = 37.8 m2<br> P = _?_

matrenka [14]

Answer:

l:9

p:16.4

Step-by-step explanation:

l x w = A

A÷w=l

37.8÷4.4=9

2l+2w=P

18+8.4=16.4

4 0

3 years ago