MATH 1113
Test #1 Chapter 2, 3.1-3.4
NAME________________________
Show all work for full credit.
1. Given: f ( x) 
x3
. (4 points)
x 1
Find: f ( x),  f ( x),
f ( x  2), and f ( x  2)
2. Determine (algebraically) whether the given function is even, odd, or neither. (3
points)
F ( x)  2 x 
x2
3
3. Determine (graphically) whether the given function is even, odd, or neither. (2
points)
4. Find the domain for each function. (4 points0
a. F ( x) 
1
x  2x  1
2
if  2  x  0
3

 1 
b. H ( x)    if 0  x  4
 x 
 x  4 if 4  x  10
5. Find the average rate of change between 0 and x for the function given. (4 points)
f ( x )  f ( 0)
(hint:
)
f ( x)  2 x 2  5 x 3
x0
6. Using techniques of shifting, compressing or stretching, and reflections, graph the
given function. Identify any intercepts on the graph. State the domain and range
for the function. (6 points)
g ( x)  2 x  3  4
7. Given: f ( x)  x  1 and
Find: ( g  g )x, and
g ( x)  1  2 x 2 (4 points)
( g  g )(1)
8. Given: f ( x)  2 x  3 and
g ( x)  4 x 2 (6 points)
Find: ( f  g )( x), ( g  f )( x), and
( f  g )( 2)
9. A circle of radius 4 is inscribed in a square (see the figure). (6 points)
a. Find the area A of the square.
(Hint: A  s 2 )
b.
Find the perimeter P of the square.
(Hint: P  4s)
10. Consider the quadratic function f ( x)  x 2  8x  3 . (10 points)
a.
Give the coordinates of the vertex of the graph of f. ________________________
b.
Give the equation of the axis of symmetry. _________________________
c.
Give the coordinates of each x-intercept. __________________________
d.
Give the coordinates of the y-intercept. __________________________
e.
Sketch the graph of f and label a-d on the graph.
f(x)
x
11. Consider the rational function g ( x) 
3x 2
. (16 points)
x2  4
a.
Determine the domain. ______________________________
b.
Give the coordinates of each x-intercept. __________________________________
c.
Give the coordinates of the y-intercept. _____________________
d.
Determine whether g is even, odd, or neither. ____________________
e.
Write the equation of each vertical asymptote. __________________________
f.
Write the equation of each horizontal or oblique asymptote and give the
coordinate pairs of each, if any, point where the graph intersects it.
____________________________________
g.
Determine the intervals where the graph is above and where it is below the xaxis.
___________________________________________________________
h. Sketch the graph of g.
g(x)
x
12. Consider the polynomial function f ( x)  2 xx  2x  1 . (10 points)
2
a.
Find the x and y intercepts of f ____________________________
b. Determine whether the graph of f crosses or touches the x-axis at each
intercept
_________________________________________________________
c.
Find the power function that the graph of f resembles for large values of x
____________
d.
Determine the maximum number of turning points on the graph of f __________
e. Graph f using intervals (x-intercepts as endpoints of the intervals)