Precalculus
Mr.Grima
CHAPTER 1 TEST REVIEW
Give the domain and range of the relation.
1) {(4, –1), (7, 2), (8, –7), (8, 6)}
12-22: Use the following graph to answer the
questions.
2-4: Determine whether the relation is a
function.
2) {(–6, 8), (–3, 8), (2, –7), (2, –9)}
3) {(–3, –5), (–1, 5), (2, –4), (7, –8)}
4)
Evaluate the function at the given value of
the independent variable and simplify.
5) f ( x ) = 5 x 2 + 2 x + 3; f ( x − 1) .
6-7: Find and simplify the difference quotient
for the given functions.
6) f ( x ) = x 2 + 9 x − 8
1
7) f ( x ) =
5x
Evaluate the piecewise function at the given
value of the independent variable.
if x > −2
⎧⎪ x − 3,
8) f ( x ) = ⎨
⎪⎩− ( x − 3 ) , if x ≤ -2
Determine f ( −3).
9-10: Determine whether or not the functions
are even, odd, or neither.
9) f ( x ) = x 3 − 5 x
10) f ( x ) = x 3 + x 2 + 4
11) f ( x ) = 4 x 2 + x 4
12) Domain
13) Range
14) x-intercepts
15) y-intercepts
16) Interval(s) on which f (x) is
increasing
17) Interval(s) on which f(x) is
decreasing
18) Interval(s) on which f(x) is
constant
19) What are the relative
minimums of f(x)?
20) At what numbers does f(x) have
a relative minimum?
21) f(2) =
22) Is f even, odd, or neither?
Use the given conditions to write an equation
for the line in point-slope form.
23) Passing through ( 4, −7 ) with
x − intercept = −4
Use the given conditions to write an equation
for the line in point-slope form.
24) Passing through ( 4, −3 ) and ( −5, −2)
25-27: Graph the equation in the rectangular
coordinate system.
25) x = 2
26) −
37) f ( x ) = 3 x + 5,
g ( x ) = 6x − 6
Find fg.
38) f ( x ) = 4 x + 3,
g ( x ) = 4 x − 16
Find fg.
1
x +y −2=0
4
39) f ( x ) =
27) −4 x − 8 y − 24 = 0
3x
,
x −1
g (x) =
5
x +9
7
,
x +1
g (x) =
4
5x
Find f + g.
28-29: Use the given conditions to write an
equation for the line in the indicated form.
28) Passing through ( 4,4 ) and parallel to the
line whose equation is 4 x + y − 4 = 0 in slopeintercept form.
40) f ( x ) =
Find f g .
41) f ( x ) = −4 x + 3,
g ( x ) = 6x + 4
Find g f .
42) f ( x ) = x ,
29) Passing through ( 4,3 ) and perpendicular to
Find f g .
the line whose equation is −3 x + y − 3 = 0 in
point-slope form.
43) f ( x ) = x + 1,
g ( x ) = 3 x + 15
g (x) =
4
x+6
Find g f .
Find the average rate of change of the
function from x1 to x2.
30) f ( x ) = −3 x − x from x1 = 5 to x2 = 6
2
44-45: Use the following graph to answer the
transform each function.
31-34: Find the domain of the function.
x
31) g ( x ) = 2
x − 16
32) f ( x ) = 19 − x
33) h ( x ) =
x
x −6
1
34) q ( x ) =
4
−3
x −2
44) g ( x ) = −2f ( x + 1)
45) h ( x ) = −f ( − x ) + 1
35-43: Given functions f and g, perform the
indicated operations and find the domain of
the resulting function.
35) f ( x ) = 7 x − 5,
g ( x ) = 2x − 4
Find f – g.
36) f ( x ) = 5 x 2 − 7 x,
Find
f
.
g
g ( x ) = x 2 −2 x − 35
46-47: Determine if the two functions are
inverses of each other.
x −3
x +3
46) f ( x ) =
, h(x) =
2
2
x −3
, g ( x ) = 2x + 3
47) f ( x ) =
2
48-51: Find the inverse of each function.
2x − 5
48) f ( x ) =
7
49) f ( x ) = ( x + 3 )
3
50) f ( x ) = x + 4
3
51) f ( x ) =
8x − 5
52-53: Graph f as a solid line and f-1 as a
dashed line in the same rectangular
coordinate plane. Find an equation for f-1.
Use interval notation to give the domain and
range of f and f-1.
52) f ( x ) = x 2 − 3, x ≥ 0
53) f ( x ) = ( x − 3 ) , x ≥ 3
2
CHAPTER 1 TEST REVIEW ANSWERS
26.
1. domain = {4,8,7};range = {−1, −7,2,6}
2.
3.
4.
5.
6.
Not a function
Function
Not a function
5x 2 − 8x + 6
2x + h + 9
−1
7.
5x ( x + h )
8. 6
9. Odd
10. Neither
11. Even
12. [ −4,4 ]
27.
13. [ −1,3 ]
14. −1,1
15. −1
16. ( 0,2 )
17. ( −2,0 )
18. ( −4, −2 ) ∪ ( 2,4 )
19. −1
20. 0
21. 3
22. even
7
( x − 4)
8
1
23
24. y = − x −
9
9
23. y + 7 = −
25.
28. y = −4 x + 20
29. y − 3 = −
1
( x − 4)
3
30. −34
31. ( −∞, −4 ) ∪ ( −4,4 ) ∪ ( 4, ∞ )
32. ( −∞,19 ]
33. ( 6, ∞ )
⎛ 10 ⎞ ⎛ 10 ⎞
⎟ ∪ ⎜ ,∞ ⎟
⎝ 3 ⎠ ⎝ 3
⎠
( −∞, ∞ )
34. ( −∞,2 ) ∪ ⎜ 2,
35. 5 x − 1
5x 2 − 7x
( −∞, −5 ) ∪ ( −5,7 ) ∪ ( 7, ∞ )
x 2 − 2 x − 35
37. 18 x 2 + 12 x − 30 ( −∞, ∞ )
36.
38.
39.
16 x 2 − 52 x − 48
3 x 2 + 32 x − 5
( x − 1)( x + 9 )
[ 4, ∞ )
( −∞, −9 ) ∪ ( −9,1) ∪ (1, ∞ )
35 x
4⎞ ⎛ 4 ⎞
⎛
−∞, − ⎟ ∪ ⎜ − ,0 ⎟ ∪ ( 0, ∞ )
⎜
4 + 5x ⎝
5⎠ ⎝ 5 ⎠
41. −24 x + 22 ( −∞, ∞ )
40.
42.
43.
44.
3 x + 15
4
x +7
[ −5, ∞ )
( −∞, −7 ) ∪ ( −7, ∞ )
46. No
47. Yes
7x + 5
2
−1
3
49. f ( x ) = x − 3
48. f −1 ( x ) =
50. f −1 ( x ) = x 2 − 4
51. f −1 ( x ) =
52.
45.
53.
3 5
+
8x 8