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2 years ago

The graphs below have the same shape. What is the equation of the blue graph?

Mathematics

1 answer:

S_A_V [24]2 years ago

5 0

<h3>Answer: Choice C. g(x) = (x-4)^2</h3>

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Explanation:

If we were to keep the red curve completely fixed, but we moved the xy axis four units to the left, then this would give the illusion the red curve is moving four units to the right to arrive at the blue curve's location.

Shifting the xy axis four units to the left is the same as subtracting 4 from each initial input x value. So we go from x to x-4.

The parent function f(x) = x^2 then becomes g(x) = (x-4)^2 which is choice C.

As one way to check, plug in x = 4 and you should find that g(4) = 0. This is the x intercept of the blue curve. Something like g(x) = (x+4)^2 does not work because plugging x = 4 into this leads to g(x) = 64, so that rules out choice A. You can eliminate choices B and D for similar reasoning as well.

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pishuonlain [190]

If the square is the window (I couldn't decipher the grammar/punctuation), the area is 64 feet squared. Since it is a square, the formula to find the area is sxs (side length times side length). 8x8=64, which makes the total area 64 square feet.

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3 years ago

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

Learn more about exponential function from brainly.com/question/13657083

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3 years ago

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Mult. the 2nd eqn by 6 and then add this "new" equation to the 1st given eqn:

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--------------------
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3 years ago

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mel-nik [20]

${\huge {\mathfrak {Answer :-}}}$

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Or, l = 13 - b

So, we may write like this,

Area = l * b

Or, l * b > 30

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Or, 13l - l^2 > 30

Or, l^2 - 13l + 30 > 0

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Or, l(l - 3) - 10(l - 3) > 0

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Step-by-step explanation:

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2 years ago

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The graphs below have the same shape. What is the equation of the blue graph?​

The graphs below have the same shape. What is the equation of the blue graph?