Problem Set 2: Functions
Math 513 - Modern Plane Trigonometry
EUGENIO E. BALASABAS MAED MATH
MATH513
I. Domain and Range of a Function
1. Each given equation defines y as a function of x. Find the domain and range.
a. y = √x
b.
𝑦 = 1/√2𝑥
c. y = x2 - 9
2. Find the domain of each given function.
a. f (x) = √ x + 5
b. g (x) = 10x
c. g (s) = s3 + 1
3. If f (x) = 3x2 - 2x + 5, evaluate the following:
a. f (-10)
b. f (3p)
c. f (a + b)
II. Operations on Functions
1. If f and g are functions defined by f (x) = 3x + 5 and g (x) = x2 , find:
a. f + g
b. f - g
c. f g
d. f / g
e. f o g
2. If s ( x ) = x + 5
and t ( x ) =
1 / x - 8 , evaluate the following:
a. s ( t ( x ) )
b. t ( s ( x ) )
c. s ( s ( -10 ) )
III. Graphs of Some Functions:
1. Find the domain and range of each of the following functions and
sketch the graph.
a.
Y = 5x - 2
b. – 10x + 1
c. y = x2 + 1
2. Determine whether each given equation is odd or even. Sketch the graph
showing the proper symmetry.
a.
y = x4 + 2
b.
c.
y = 2x