Which function is represented in this graph?
2 answers:
Answer:
y = tan (1/2 x - π/2) ⇒ the answer is (b)
Step-by-step explanation:
* Lets talk about the tangent function
- The tangent has a period of π, with each period separated by
a vertical asymptote. The concept of "amplitude" doesn't
really exist because -∞ < y < ∞
- You can transform the graph for tangent
∵ y = A tan B(x + C) + D
* Where:
# A, changes amplitude. (A always = 1)
# B determines the period.
# C determines how the graph is shifted from left to right.
(horizontally)
# D determines how the graph is shifted up or down.(vertically)
∵ The basic function is y = tanФ has an amplitude of 1.
It has a period of π. It has no phase or vertical shifts,
because it is centered on the origin.
* Look to the problem
- From the graph:
- The period is 2π
∵ Period = π/B
∴ 2π = π/B ⇒ ÷ π
∴ 2 = 1/B
∴ B = 1/2
- the starting point of the function is at π instead of zero
∴ It moves π units to the right
∴ C = -π
∴ y = tan 1/2(x - π)
∴ y = tan (1/2 x - π/2)
* The function is ⇒ y = tan (1/2 x - π/2)
* The blue represents y = tanx
The red represents y = tan (1/2 x - π/2)
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The product of a <em>complex</em> number and its conjugate is (a + i b) · (a - i b), where a and b are <em>real</em> numbers, and the result for the <em>complex</em> number 2 + i 3 is 13.
<h3>What is the multiplication of a complex number and its conjugate</h3>Let be a <em>complex</em> number a + i b, whose conjugate is a - i b. Where a and b are <em>real</em> numbers. The product of these two numbers is:
(a + i b) · (a - i b)
Then, we proceed to obtain the result by some algebraic handling:
a · (a + i b) + (- i b) · (a + i b)
a² + i a · b - i a · b - i² b²
a² - i² b²
a² + b²
If we know that a = 2 and b = 3, then the product of the complex number and its conjugate is:
To learn more on complex numbers: brainly.com/question/10251853
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