MATH 1090 Sec. 5
Section 2.4: Special Functions and Their Graphs
(1) The identity function: y=f(x) = x
(2) Constant functions: y=f(x) = C, where Cis a constant.
(3) Power functions: y=f(x) = axb, where b > 0.
Ex.
(a) Root functions : y=f(x) = axb(0 < b < 1) or ac
√x=ax1/c(c > 1)
(b) Polynomial functions : y=f(x) = axb,where bis a natural number ≥1
In general, a polynomial function of degree n:
y=f(x) = anxn+an−1xn−1+· ·· +a1x+a0,
where an6= 0.
(i) Linear functions = polynomial functions of degree 1
(ii) Quadratic functions = polynomial functions of degree 2
(4) Rational functions: y=f(x) = h(x)
g(x)with g(x)6= 0, where h(x) and g(x) are polynomials.
The domain of rational functions is the set of all real numbers for which g(x)6= 0.
(a) Reciprocal function: y(x) = f(x) = 1
x.
(5) Piecewise defined functions: defined by more than one functions with specific domain for each.
Ex. For Sas selling price (dependent variable) and Cas cost (independent variable),
S=f(C) = 3Cif 0 ≤C≤20
1.5C+ 30 if C > 20
(a) Absolute value function: y=f(x) = |x|or f(x) = xif x≥0
−xif x < 0
Note: See the handout “2.4 Graphs” for the graph of each type of function.
General Polynomial Graphs
Degree 2 3 4
Turning points
x-intercepts
Possible shapes
1
