Math 260 (Precalculus)
Find
Chapter 2 practice Test
f a  h  f a 
h
for f  x  
x
, f  x   2x  5
x6
Find the domain of the function. (Enter your answer using interval notation.)
G  x   x2  4 , g  x  
x4
2 x
, g  x   4 x 2  3x , f  x  
1 x
2 x
Sketch the graph of the function by first making a table of values.
G(x) = |x| + x, G(x) = |x| − x
Sketch the graph of the piecewise defined function.
 0 if x  4 
f  x  
,
 5 if x  4 
 4  x2
f  x  
 x
if x  2 

if x > 2 
The graph of a piecewise defined function is given. Find a formula for the function in the
indicated form.
Determine whether the equation defines y as a function of x.
x = y2
x2 + (y − 3)2 = 5,
5x + |y| = 0
x + y2 = 4,
x2 + y = 5,
x2y + y = 5,
x  y  14
Find a function whose graph is the given curve.
The line segment joining the points (−3, −2) and (5, 3).
The bottom half of the circle x2 + y2 = 81
Consider a function f(x) = x3 − 3x and g(x) = x4 − 5x3 − 6x2
a. Find the local maximum and minimum values of the function and the value of x at
which each occurs.
b. Find the intervals on which the function is increasing and decreasing.
The average rate of change of a function f between x = g and x = b is:
The average rate of change of the linear function f(x) = 6x + 4 between any two points is:
A function is given. Determine the average rate of change of the function between the given
values of the variable:
h(t) = t2 + 3t; t = −1, t = 5
f(x) = 3x2; x = 5, x = 5 + h
f(x) = 7 − x2; x = 2, x = 2 + h
g  x 
7
; x  0, x  h
x2
Sketch the graph of the function. (Indicate all intercepts.)
f  x   x  4  2 , f  x  x  3  2 , y  4 
1
1
2
 x  2 , y  4  x  4
2
2
A function f is given, and the indicated transformations are applied to its graph (in the given
order). Write the equation for the final transformed graph.
f(x) = |x|; shift 7 units to the right and shift upward 6 units
f  x   4 x ; reflect in the y-axis and shift upward 9 units
f(x) = x2; shift 9 units to the left and reflect in the x-axis
f(x) = x2; stretch vertically by a factor of 9, shift down 5 units, and shift 3 units to right.
f(x) = |x|; shrink vertically by a factor of
1
shift to left 9 units, and shift upward 3 units.
3
The graphs of f and g are given. Find a formula for the function g.
The graph of y = f(x) is given. Match each equation with its graph.
y = f(x − 9),
y=
y = f(x) + 6,
y = 2f(x + 6),
y = −f(5x)
1
f  x  , y = −f(x + 4), y = f(x − 4) + 4, y = f(−x)
3
Determine whether the function f is even, odd, or neither.
f(x) = x6 + x, f(x) = x7 – x, f(x) = x3 + 3x- 5, f(x) = x +
1
x
Let f(x) = x2 + 4x, g(x) = 5x2 – 1
Let
f  x   9  x2 , g  x   1  x
4
x
, g  x 
x3
x3
f
Find the domain of
 x  (Enter your answer using interval notation.)
g
Let f  x  
Find the domain of the function. (Enter your answer using interval notation.)
f  x 
x5
x 1
Use f(x) = 5x − 3 and g(x) = 2 − x2
to evaluate the expression. f(g(-2)), g(f(3)) ,(f ○ g)(x), (f ○ g)(x)
Use the given graphs of f and g to evaluate the expression f(g(1)) & g(f(3))
Consider the following functions.
f  x 
x
, g  x   2x  5
x5
Find (f ○ g)(x), (g ○ f)(x) and domain of each composition.
A function f has the following verbal description: "Multiply by 10, add 1, and then take
the third power of the result." Find algebraic formulas that express f and f −1
in terms of the input x.
True or false?
(a) If f has an inverse, then f −1(x) is the same as
1
. Ture/false?
f  x
(b) If f has an inverse, then f −1(f(x)) = x. Ture/false?
The graph of a function f is given. Determine whether f is one-to-one.
Determine whether the function is one-to-one.
2x , f(x) = |5x|, h(x) = x2 − 5x,
f(x) = −4x + 1, f(x) =
4
4
, f  x 
2
x
x
f(x) =
Use the Inverse Function Property to determine whether f and g are inverses of each other.
f(x) = 7x;
g(x) =
x
7
f(x) = 7x − 6;
g(x) =
x6
7
x 3
;
5x  2
g(x) =
3  2x
1  5x
f(x) =
Find the inverse function of f.
f(x) = 6x + 1, f(x) = 9 − 2x3
f  x 
x2
, f(x) =
x2
4  7x