Please help me with this translating trigonometry graphs question. Brainliest and Points Available.
1 answer:
According with the definition of translation, we conclude that the equations of graphs M and N are m(x) = f(x - 5) and n(x) = f(x) - 2, respectively.
<h3>How to apply translations on a given function</h3>
<em>Rigid</em> transformations are transformation such that the <em>Euclidean</em> distance of every point of a function is conserved. Translations are a kind of <em>rigid</em> transformations and there are two basic forms of translations:
Horizontal translation
g(x) = f(x - k), k ∈ (1)
Where the translation goes <em>rightwards</em> for k > 0.
Vertical translation
g(x) = f(x) + k, k ∈ (2)
Where the translation goes <em>upwards</em> for k > 0.
According with the definition of translation, we conclude that the equations of graphs M and N are m(x) = f(x - 5) and n(x) = f(x) - 2, respectively.
To learn more on translations: brainly.com/question/17485121
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Answer:
When we have a rational function like:
The domain will be the set of all real numbers, such that the denominator is different than zero.
So the first step is to find the values of x such that the denominator (x^2 + 3) is equal to zero.
Then we need to solve:
x^2 + 3 = 0
x^2 = -3
x = √(-3)
This is the square root of a negative number, then this is a complex number.
This means that there is no real number such that x^2 + 3 is equal to zero, then if x can only be a real number, we will never have the denominator equal to zero, so the domain will be the set of all real numbers.
D: x ∈ R.
b) we want to find two different numbers x such that:
r(x) = 1/4
Then we need to solve:
We can multiply both sides by (x^2 + 3)
Now we can multiply both sides by 4:
Now we only need to solve the quadratic equation:
x^2 + 3 - 4*x - 4 = 0
x^2 - 4*x - 1 = 0
We can use the Bhaskara's formula to solve this, remember that for an equation like:
a*x^2 + b*x + c = 0
the solutions are:
here we have:
a = 1
b = -4
c = -1
Then in this case the solutions are:
x = (4 + 4.47)/2 = 4.235
x = (4 - 4.47)/2 = -0.235