Download N2-2_-_More_About_Funtions

N2-2
Topic: More About Functions
Determining Domain and Intercepts from an Equation
If the domain of a function in equation form is not expressed, it is
implied to be the largest set of real numbers that have a real output.
When determining the implied domain from an equation, there are
only three expressions that can cause restrictions:
a
1) f(x)  , b  0
b
2) f(x)  a, a  0
3) f(x) = logb a, a > 0
Other restrictions can be implied by real-world situations (e.g.,
distance cannot be negative, number of people must be whole
numbers, etc.)
For each of the following functions, determine the domain and
intercepts from the equation.
1. F(x) = 5x2 + 4x - 1
Domain:
x-intercept(s):
y-intercept:
2. g(x) =
3x
x5
x-intercept(s):
y-intercept:
x-intercept(s):
y-intercept:
Domain:
3. h(x) =
Domain:
x4
Using Function Notation
4. Evaluate each of the following for f ( x )  x 2  2x .
a) f(2)
b) f(-3)
c) f(2x)
d) -f(x)
e) f(-x)
f) f(x+2)
g) Is f(x+2) = f(x) + f(2)?
Analyzing a Function from the Equation
5. Answer the following questions about the function: f(x) = x  3
x2
a) What is the domain of f? ___________
b) What is f(-1)? _____ What point is on the graph of f?________
c) Where does f(x) = 2? ________ Name the ordered pair. ______


d) Is the point 1, 1  on the graph of f?__________
2

e) Where would the graph of f cross the axes? ________
f) What is f(-x)? __________
g) What is –f(x)? __________