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2 years ago

Consider the three functions below.

Mathematics

2 answers:

andrew11 [14]2 years ago

8 0

Answer:

The range of g(x) is y > 0

The ranges of f(x) and h(x) are different from the range of g(x)

Step-by-step explanation:

we have

$f(x)=-(\frac{6}{11})^{x}$

$g(x)=(\frac{6}{11})^{-x}$

$h(x)=-(\frac{6}{11})^{-x}$

Using a graphing tool

see the attached figure

Verify each statement

case A) The range of h(x) is y > 0.

The statement is false

The range of h(x) < 0

case B) The range of g(x) is y > 0. (Note the statement is The range of g(x) is y > 0 instead of The domain of g(x) is y > 0)

The statement is true (see the attached figure)

case C) The ranges of f(x) and h(x) are different from the range of g(x)

The statement is true (see the attached figure)

Because

The ranges of f(x) and h(x) are y < 0

and

The range of g(x) is y > 0

case D) The domains of f(x) and g(x) are different from the domain of h(x)

The statement is false

The domain of the three functions is the same

skad [1K]2 years ago

3 0

Answer:

OPTION C.The ranges of f(x) and h(x) are different from the range of g(x).

Step-by-step explanation:

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Find the standard form of the equation of the parabola with a focus at (3, 0) and a directrix at x = -3.

Nikitich [7]

Check the picture below.

now, keep in mind that the focus point is at 3,0 and the directrix is to the left-hand-side of it, therefore, is a horizontal parabola, and it opens to the right-hand-side, like in the picture.

keep in mind that the vertex is half-way between the focus point and directrix, at a distance "p" from either one, notice the "p" distance is just 3 units, since the parabola is opening to the right, "p" is positive.

$\bf \textit{parabola vertex form with focus point distance}\\\\
\begin{array}{llll}
\boxed{(y-{{ k}})^2=4{{ p}}(x-{{ h}})}
\\\\
(x-{{ h}})^2=4{{ p}}(y-{{ k}})
\end{array}
\qquad 
\begin{array}{llll}
vertex\ ({{ h}},{{ k}})\\\\
{{ p}}=\textit{distance from vertex to }\\
\qquad \textit{ focus or directrix}
\end{array}\\\\
-------------------------------\\\\
\begin{cases}
h=0\\
k=0\\
p=3
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2 years ago

Which statement identifies how to show that j(x) = 11.6ex and k(x) = In (StartFraction x Over 11.6 EndFraction) are inverse func

Vadim26 [7]

Answer:

<h2>It must be shown that both j(k(x)) and k(j(x)) equal x</h2>

Step-by-step explanation:

Given the function j(x) = 11.6 $e^x$ and k(x) = $ln \dfrac{x}{11.6}$ , to show that both equality functions are true, all we need to show is that both j(k(x)) and k(j(x)) equal x,

For j(k(x));

j(k(x)) = j[(ln x/11.6)]

j[(ln (x/11.6)] = 11.6e^{ln (x/11.6)}

j[(ln x/11.6)] = 11.6(x/11.6) (exponential function will cancel out the natural logarithm)

j[(ln x/11.6)] = 11.6 * x/11.6

j[(ln x/11.6)] = x

Hence j[k(x)] = x

Similarly for k[j(x)];

k[j(x)] = k[11.6e^x]

k[11.6e^x] = ln (11.6e^x/11.6)

k[11.6e^x] = ln(e^x)

exponential function will cancel out the natural logarithm leaving x

k[11.6e^x] = x

Hence k[j(x)] = x

From the calculations above, it can be seen that j[k(x)] = k[j(x)] = x, this shows that the functions j(x) = 11.6 $e^x$ and k(x) = $ln \dfrac{x}{11.6}$ are inverse functions.

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2 years ago

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Reika [66]

Answer:

You can use a calculator for the decimal operations, but practice some by hand because on the quiz and the test you will not have a calculator.

Step-by-step explanation:

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2 years ago

What are three collinear points on line l?

Jet001 [13]

Points A, F, and G are three collinear points on line l.

$\boxed{ \ The \ Answer \ is \ B \ }$

<h3>Further explanation </h3>

Let us consider the definition of collinear.

Collinear

Collinear points represent points that lie on a straight line. Any two points are always collinear because we can constantly connect them with a straight line. A collinear relationship can occur from three points or more, but they don’t have to be.

Noncollinear

Noncollinear points represent the points that do not lie in a similar straight line.

Given that lines k, l, and m with points A, B, C, D, F, and G. The logical conclusions that can be taken correctly based on the attached picture are as follows:

At line k, points A and B are collinear.
At line l, points A, F, and G are collinear.
At line m, points B and F are collinear.
Point A is placed at line k and line l.
Point B is placed at line k and line m.
Point F is located at line l and line m.
Points C and D are not located on any line.

Hence, the specific answer to this key question is undoubted, i.e., points A, F, and G.

All points can, also, be said to be coplanar. This is because the three lines intersect with each other and lie on a planar surface.

Coplanar

Coplanar points represent a group of points that lie on the same plane, i.e. a planar surface that extends without end in all directions. Any two or three points are always coplanar, but four or more points might or might not be coplanar.

<h3>Learn more </h3>

Determine which points are coplanar and noncollinear brainly.com/question/4165000
Finding a set of points is not coplanar in a pyramid brainly.com/question/2269323
Determining the best description of connection lines AB and CD on given rectangular prism ABCD brainly.com/question/4910705

Keywords: what are, three collinear points A, F, and G, noncollinear, located, similar straight line, definition, represents, relationship, coplanar

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2 years ago

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