Intermediate Algebra Problems With Answers - Sample 4

A set of intermediate algebra problems on functions, domain, range, collinear points, zeros of functions, x and y intercepts, ... with answers, are presented. The solutions are at the bottom of the page.

Find the constant b so that the three points A(2 , 3), B(4 , 7) and C(8 , b) are collinear (i.e. on the same line).

Which of the following equations represent y as a function of x?
a) x^{ 2} + y = 5
b) x^{ 2} - 7x + y^{ 2} = 0
c) x^{ 2} - y^{ 3} - 9 = 0
d) |x| - |y| = 0

Which set of ordered pairs represents a function?
a) A = { (a , 3) , (b , 5) , (c , 9) , (d , 9) }
b) B = { (a , -3) , (b , 6) , (c , 1) , (b , 9) }
c) C = { (a , 3) , (b , 3) , (c , 3) , (d , 3) }
d) D = { (a , 5) , (a , -9) , (a , 0) , (a , 12) }

Find the domain of each function.
a) f(x) = 1 / (x - 2)
b) g(x) = √(x + 5)
c) h(x) = 3 / √(x - 4)
d) j(x) = 1 / [ (x + 1)(x -7) ]

Find the zeros of each function.
a) f(x) = 3 - 5/x
b) g(x) = √(x - 1)
c) h(x) = | x - 9 | - 4
d) i(x) = | x - 9 | + 7
d) j(x) = x^{ 2} - 16
d) k(x) = x^{ 2} + 3

Find the range of each function.
a) f(x) = x^{ 2}
b) g(x) = | x |
c) h(x) = x^{ 2} + 6
d) j(x) = | x | + 2

Let f(x) = 2x^{ 2} - 4x + 4 and h(x) = 2x - 4. Find
a) f(2) =
b) h(5) =
c) f(3) + h(3) =

Find the x and y intercepts of the graphs of the following equations.
a) 2x + 4y = 5
b) x^{ 2} + (y - 3)^{ 2} = 9
c) |x - 3| + |5 - y| = 6

Find the linear function f(x) = A x + B such that f(2) = 1 and f(4) = -3.

Which of these functions is even?
a) f(x) = -x^{ 2} + 7
b) g(x) = | x - 6 |
c) h(x) = x^{ 3} + 9
d) j(x) = | x | + 1