Name__________________________________________ Date___________________
Calculus I Honors – Precalculus Review Period________
Section I: Linear Functions
Slope-Intercept Form:
y mx b
Point-Slope Form:
11
y y m x x
1. Write the equation of each line in point-slope form:
a. given a point and the slope:
1, 2 3m
b. given two points:
1, 3 7,1
c. given the point
1, 2
and is perpendicular
to the line
2 3 1yx
.
d. given the point
1, 2
and is parallel to the
line
3 2 1xy
.
2. Sketch a line with the given slope.
a.
0m
b.
0m
c.
0m
d.
mundefined
Section II: Functions and Relations
3. Determine the domain and range of each relation. Then decide if the relation is a function.
a.
(3,1),(2, 3),( 1,5),( 2, 2),(0,2)}
b.
c.
d.
e.
f.
4. For
2
7f x x
, find
a.
1f
b.
4fc
c.
1fb
d.
( ) ( )f x x f x
x
;
0x
5. Find domain for each of the following. Write your answer in interval notation.
a.
( ) 1f x x
b.
1
21
hx
x
c.
2
25g x x
d.
1
12
jx
x
e.
5
( ) 3 5f x x
f.
2
4
1
fx
x
6. Use the graph given to the right to answer the following questions:
a. Identify the domain and range of f.
b. Identify the domain and range of g.
c. Identify the value of
3f
.
d. Identify the value of
0g
.
e. Estimate the solution(s) of
2fx
.
f. Estimate the solution(s) of
0.gx
g. Estimate the
x
-coordinates for which
f x g x
.
h. Estimate the value of
1fg
.
i. Estimate the value of
3gf
.
Section III: Parent Functions
7. Match each parent function with the correct graph. Identify all key features of each parent graph.
1
fx
x
2
1
gx
x
h x x
2
i x x
j x x
3
k x x
3
l x x
log
a
m x x
x
n x a
p x x
a. b.
Function: Function:
Domain: Range: Domain: Range:
Extrema: Extrema:
Increasing: Decreasing: Increasing: Decreasing:
Asymptotes: Asymptotes:
f
-5 -4 -3 -2 -1 1 2 3 4 5
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
x
y
g
c. d.
Function: Function:
Domain: Range: Domain: Range:
Extrema: Extrema:
Increasing: Decreasing: Increasing: Decreasing:
Asymptotes: Asymptotes:
e. f.
Function: Function:
Domain: Range: Domain: Range:
Extrema: Extrema:
Increasing: Decreasing: Increasing: Decreasing:
Asymptotes: Asymptotes:
g. h.
Function: Function:
Domain: Range: Domain: Range:
Extrema: Extrema:
Increasing: Decreasing: Increasing: Decreasing:
Asymptotes: Asymptotes:
i. Function:
Domain: Range:
Extrema:
Increasing: Decreasing:
Asymptotes:
Section IV: Simplifying Expressions
8. Perform the operation indicated and simplify each expression. Identify any domain restrictions.
a.
22
2
4
23
x x x
x x x
b.
2
2
6 9 9
93
x x x
xx
c.
22
42
93x x x
d.
4
2
2
x
x
x
e.
1
1
1x
x
f.
11
22x
x
g.
2
1
1
x
x
x
x
9. Given:
( ) 3f x x
and
2
5
()
2 15
x
gx
xx
, a) perform the given operation and write the answer in
simplified form, and b) find the domain of the combination of functions.
a.
( ) ( )f x g x
b.
( ) ( )g x f x
c.
( ( ))g f x
d.
()
()
fx
gx
10. Rationalize each function and simplify.
a.
4
x
x
b.
42
x
x
c.
4
2
x
x
Section V: Exponential and Log Functions
11. Rewrite each function in rational form. Simplify if necessary.
a.
23
x
b.
32
x
c.
23
x
d.
2
43
3x
x
12. Rewrite each function in exponential form. Simplify if necessary.
a.
5
4
x
b.
5
2
x
c.
6
3
x
d.
35
2
4xx
13. Condense and write as a single logarithm.
a.
44
log 3 5log x
b.
log3 5logx
c.
ln2 4ln 3ln ln8xy
d.
1
2ln4 ln ln 3ln2
2
xy
14. Expand each logarithmic expression.
a.
7
4
5
log
x
y
b.
3
2
log
9
x
y
c.
4
ln27 a
d.
2
32
31
ln
23
x
xx
Section VI: Piecewise Functions
15. Graph each function, then evaluate each at the given value.
a.
2
,0
4, 0 3
2 6, 3
xx
f x x
xx
5f
3f
1f
10f
b.
2
2, 1
, 1 2
2 , 2
xx
g x x x
xx
5g
1g
0g
5g
16. Evaluate each function at the given value.
a.
2
2 3, 0
, 0 2
1, 2
xx
h x x x
x
1h
0h
1.5h
2h
b.
3 2, 2
1, 2 0
,1
xx
j x x
xx
4j
0j
1
2
j
9j
17. Write the equation of the piecewise function graphed below.
Section VII: Intercepts and intersection of graphs
18. For each function, find all x- and y-intercepts. Write as ordered pairs.
a.
2
( ) 5 66f x x x
b.
22
( ) 25g x x x
c.
2
2
9
()
4 21
x
hx
xx
19. Find the points of intersection of the graphs of each set of functions.
a.
2
4 and 6x y x y
b.
2
2 8and 8x x y x y
Section VIII: Solving Equations
20. Solve each equation by factoring, completing the square or quadratic formula.
a.
2
49 0x
b.
2
5 36 0xx
c.
2
2 15 0xx
d.
3
4 25 0xx
e.
2
3 13 10xx
f.
2
3 6 0xx
