Complex Numbers
Identify the real and imaginary part of the number.
3+4i
Real = 3, Imaginary = 4
Consider f(x) = x2
If g(x) = (x-3)2
What is the transformation?
3 in the positive x-direction
Consider the function
f(x) = 2 + x2
What is the domain and range?
All real numbers
What is the inverse of the function
f(x) = x?
f-1(x)=x
Consider the function
f(x) = (x+2)2 - 4
What is the vertex?
Vertex: (-2,-4)
What is the complex conjugate of
7-i
7+i
Consider f(x) = 2x
If g(x) = 2x + 1
What is the transformation?
1 in the positive y-direction
Consider the function
f(x) = 1/x
What is the domain?
(-∞ ,∞ )
What is the inverse of the function
f(x) = x2
f-1(x) = √x
Which of the following is NOT a plynomial?
f(x) = (5-x)3
g(x) = √x
g(x) is NOT a polynomial. Polynomials only have an interger degree.
What is
(1+i)-(3-2i)
(in a +bi form)
-2+3i
Consider f(x) = x3
If g(x) = (x/3)3
What is the transformation?Consider the function
f(x) = ex
What is the domain and range?
Domain: (-∞ ,∞ )
Range: (-∞ ,∞ )
What is the invers of the function
f(x) = x2 - 2
f-1(x) = √2+x
Consider the following graph...
How many roots are there?
4
Multiply and put in a+bi form
(2+i)(1-i)
Consider f(x) = 1/x
If g(x) = -1/x
What is the transformation?
Reflection across x and y axis
Consider the function
f(x) = 1/x2
What is the domain and range?
Domain: (-∞ ,∞ )
Range: (0,∞ )
What is the inverse of the function
f(x) = (3-x)/(9-6x+x2)
f-1(x) = -(x-3)
What is the discriminant of the following
2x2-10x+3 = 0
52
Solve and put in a+bi form:
(1+i)(2-i)+(1-i)
4+0i
Consider f(x) = 2x2 +12x + 18
If g(x) = (x+2)2 - 3
What is the transformation?
Vertical stretch and horizontal shift by -1
Consider the function
f(x) = (1+x)/(x2+2x+1)
What is the domain and range?
Domain: (-∞ ,-1)U(-1,∞ )
Range: (-∞ ,0 )U(0,∞ )
Consider the function
f(x) = (2-x)/(x2-x-2)
What is f(1) and f-1(1)
f(1) = -1/2
f-1(1) = 0
A ball is thrown into the air and has a trajectory
h(t) = -3t2 + 12t - 7
What is the maximum height of the ball? (height is in meters)
5 meters