Sample test!!
1) Give the domain, range
and zeros of the following graph:
2) Give the domain, range
and zeros of the function: f(x) = 5x/(3x - 2)
3) Sketch the graph
and use the graph to find the range and zeros of the function:
f(x) = x3 + 4x2 - x - 4
4) Let f(x) = 4x, g(x)
= x2, h(x) = x + 5 and j(x) = 2x. Find each.
a) (f + h)(x)
b) (j - f)(x)
c) f(g(h(x)))
d) g(h(j(x)))
e) (f/g)(x)
f) g(f(h(2)))
5) Sketch the graphs
of y = x2 -4, y = 4 - x2 and y = |4 - x2|
on the same axes.
6) Test each equation
for all 4 symmetries.
a) x2 - xy = 3
b) x2 - y2 = 1
c) y = -|x|
7) Use symmetry to
sketch the graph of xy2 = 2
8) Sketch each of the
following by using stretching/shrinking and/or translation.
a) y - 5 = 2|x - 1|
b) y + 3 = -(x + 1)2
9) Prove that f(x)
= (x+1)/2 and g(x) = 2x - 1 are inverse functions.
10) Sketch the graph
of f and f -1. Then find a rule for the inverse.
f(x) = x2 - 2,
x < 0
11) a) Let P(x,
y) = 2x + 2y. Let y be constant at y = 2, y = 3, y = 4. Graph
these functions.
b) Now let P be constant at P = 10, P = 12 and P = 14.
Graph these functions.
12) The area of a triangle
is a function of the base b and height h.
a) Express A as a function of b and h.
b) Find A(2,3) and A(5,6)
c) Draw the curve of constant area A(b, h) = 5 in a bh-plane.
13) let f(x) be the
following graph: 
a) What is the fundamental period for the above graph?
b) What is f(1)? f(2)?
f(3)? f(4)?
c) What is f(99)? f(13)?
f(-2)? f(-11)?
d) Graph 2f(x)
e) Graph f(2x)
f) Graph -f(x)
g) Graph f(-x)
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