Vocabulary
The set of all possible input values (x-values) of a function.
What is domain?
The domain of f(x)=x^2+3
What is all real numbers?
(2x^2+3x)+(x^2−x+4)
3x^2+2x+4
i^2
-1
y=f(x) up by 4 units
Shift graph of y=f(x) up by 4 units
The answer you get when you multiply two polynomials
What is product?
Range of f(x)=the square root of x and −1
[0,∞)
(x+2)(x−3)
x^2−x−6
(3+4i)+(1−2i)
4+2i
What does y=−f(x) do to the graph?
Reflection about the x-axis.
The imaginary unit
Domain of f(x)=1/x-5
(−∞,5) (5,∞)
x^3+6x^2+11x+6/x+1
x^2+5x+6
(2+3i)(1−i)
2+i−3i^2=2+i+3=5+i
Effect of f(x−2)
Shift the graph 2 units to the right.
A vertical or horizontal shift, stretch, compression, or reflection of a graph.
What is transformation?
Range of f(x)=−x^2+4
(−∞,4]
x^2+7x+12
(x+3)(x+4)
(2+i)(2−i)
4−i^2=4+1=5
Effect of y=f(2x)
Horizontal compression by a factor of 1/2.
The set of all possible output values (y-values) of a function.
What is range?
Range of f(x)=2x+1
(−∞,∞)
(x−2)(x^2+3x+4)
x^3+x^2-2x-8
3+i/2-i
1+i
What does y=f(x−1) do to the graph?
Shifts the graph right by 1 unit.