Multiply (x^2 - 3x + 4)(-2x^2 + 4x - 1) Show the steps on how to solve please.
1 answer:
You might be interested in
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)
Answer:
A = 68 unit^2
Step-by-step explanation:
Given:-
The piece-wise function f(x) is defined over an interval as follows:
f(x) = { x^2+3x+4 , x < 3
f(x) = { x^2+3x+4 , x≥3
Domain : [ -3 , 4 ]
Find:-
Find the area of the region enclosed by f(x) and the x axis
Solution:-
- The best way to tackle problems relating to piece-wise functions is to solve for each part individually and then combine the results.
- The first portion of function is valid over the interval [ -3 , 3 ]:
- The area "A1" bounded by f(x) is given as:
Where, The interval of the function { -3 , 3 ] = [ a , b ]:
- Similarly for the other portion of piece-wise function covering the interval [3 , 4] :
- The area "A2" bounded by f(x) is given as:
Where, The interval of the function { 3 , 4 ] = [ a , b ]:
- The total area "A" bounded by the piece-wise function over the entire domain [ -3 , 4 ] is given:
A = A1 + A2
A = 42 + 26
A = 68 unit^2