Pre-Calc Chapter 1 Sample Test
1. Use the graphs of f and g to evaluate the function.
f ( x)
(f o g)(-0.5)
A) 2 B) 1
g ( x)
C) –1
D) 0 E) 4
2. Plot the points and find the slope of the line passing through the pair of points.
(2, –3), (–4, 5)
A) slope:
4
3
B) slope: –
5
9
C) slope: –
3
4
D) slope:
3
4
E) slope: –
4
3
3. Evaluate the indicated function for f (x) = x2 + 4 and g (x) = x + 3.
( f − g )(t + 2)
A) t2 + 3t + 9 B) t2 + 5t + 3 C) t2 − t + 3 D) t2 + 3t + 3 E) t2 + 5t + 9
4. Given x2 + y2 = 15, use the algebraic tests to determine symmetry with respect to both axes and the
origin.
A) x-axis, y-axis, and origin symmetry
D) origin symmetry only
B) no symmetry
E) y-axis symmetry only
C) x-axis symmetry only
5. Determine whether lines L1 and L2 passing through the pairs of points are parallel, perpendicular, or
neither.
L1 : (9, 6), (–5, –4)
L2 : (0, 9), (–7, 4)
A) parallel B) perpendicular C) neither
6. Find all real values of x such that f (x) = 0.
f ( x) = 64 x 2 − 9
8
9
A) ±
B) −
3
64
C) ±
9
64
D)
3
8
E) ±
3
8
7. Assume that y is directly proportional to x. If x = 32 and y = 24 , determine a linear model that relates y
and x.
2
4
3
3
3
A) y = x B) y = x C) y = x D) y = x E) y = x
3
3
5
2
4
8. Which function does the graph represent?
A)
B)
C)
D)
E)
9. Use the graph of
to write an equation for the function whose graph is shown.
A)
B)
C)
D)
E)
10. During math class, a fly lands on your graph paper. It lands at a point seven units from the left side of
the paper and two units from the bottom of the paper. Before it flies away, it walks in a straight line to
a point three units from the left side of the paper and ten units from the bottom of the paper. How far
did the fly walk? Round to the nearest unit.
A) 11 units B) 12 units
C) 10 units
D) 81 units
11. Find a mathematical model for the verbal statement:
" w varies directly as the square of v and inversely as p ."
kv 2
A) w =
p
B) w = k ( vp )
2
⎛v⎞
C) w = k ⎜ ⎟
⎝ p⎠
2
⎛ p⎞
D) w = k ⎜ ⎟
⎝v⎠
2
E) w = kv 2 p
E) 9 units
12. Use the graph of the function to find the domain and range of f.
A)
B)
C)
D)
E)
13. Write the height h of the rectangle as a function of x.
A)
B)
C)
D)
E)
14. The polygon is shifted to a new position in the plane. Find the coordinates of the vertices of the
polygon in its new position.
A)
B)
C)
D)
none of these
E)
15. Find the domain of the function.
8w
w–6
A) all real numbers
B) all real numbers w ≠ 6 , w ≠ 0
C) w = 6, w = 0
g ( w) =
D) all real numbers w ≠ 6
E) w = 6
16
14
12
10
8
6
4
0
Jul
Aug
Sep
Oct
Nov
Dec
2
Jan
Feb
Mar
Apr
May
Jun
Net profit (in thousands of dollars)
16. The graph shows the net profit (in thousands) for Deepti's landscaping business for the past year.
Month
Use slopes to determine the month in which the net profit showed the greatest increase.
A) February B) July C) September D) June E) January
17. Find the inverse function of f ( x) = –7 x + 5
A)
x–5
g ( x) = –
7
B)
1
g ( x) = – x – 5
7
C)
x
g ( x) =
5
D)
E)
x +5
7
g ( x) = 5 x – 7
g ( x) = –
18. Find ( f / g )(x).
f ( x) = 2 x 2 + 8 x
g ( x) = –5 − x
A)
2x + 8
( f / g )( x) =
, x≠0
–5
B)
2 x2 + 8x
( f / g )( x) =
, x ≠ –5
–5 − x
C)
2 x2
( f / g )( x) = –
– 8, x ≠ 0
5
D)
E)
( f / g )( x) =
2 x2 + 8x
, x≠5
–5 − x
( f / g )( x) =
2 x2 + 8x
, x≠0
–5 − x
19. Which equation does not represent y as a function of x?
A) y = 7 + 2 x
20.
B) x = –y – 4 C) y = –x + 4 D) y = |6 + 8x2|
E) x = –3
After determining whether the variation model below is of the form y = kx or y =
k
, find the value of
x
k.
x
y
A) k =
13
3
195
208
45
48
3
1
B) k =
C) k =
13
13
234
54
221
51
D) k =
13
45
247
57
E) k = 13
21. Determine whether the function has an inverse function. If it does, find the inverse function.
f ( x) = x 2 + 1
A) f −1 ( x) = x + 1, x ≥ 0
B) f −1 ( x) = x − 1
C)
D) No inverse function exists.
E)
f −1 ( x) = x + 1, x ≥ −6
f −1 ( x) = x − 1
22. Use the position equation s = −16t2 + v0t + s0 to write a function that represents the situation and give
the average velocity of the object from time t1 to time t2.
An object is thrown upward from a height of 100 feet at a velocity of 37 feet per second.
t1 = 1, t2 = 5
A) s = −16t 2 + 37t + 100 ;
B) s = −16t 2 + 100t + 37 ;
C) s = −16t 2 + 37t + 100 ;
D) s = −16t 2 + 37t + 100 ;
E) s = −16t 2 + 100t + 37 ;
avg. velocity = –236 ft/s
avg. velocity = 64 ft/s
avg. velocity = –59 ft/s
avg. velocity = 1 ft/s
avg. velocity = 4 ft/s
23. Find the distance between the points. Round to the nearest hundredth, if necessary.
(–5, –9), (–4, 3)
A) 6.08 B) 8.06 C) 15 D) 12.04 E) 10.82
24. Which graph represents the function?
A)
B)
C)
D)
E)
25.
Use the functions given by f ( x) =
x
+ 1 and g ( x) = x3 to find the indicated value.
8
( f D g ) −1 (5)
A) 2 3 6
B) undefined C) 2 3 4
D)
637
512
E) 2 3 5 – 1
26. Find ( f − g )(x).
f ( x) = –
A)
B)
C)
5x
9x – 2
( f − g )( x) =
g ( x) = –
5
x
–5 x 2 + 45 x + 10
9 x2 – 2 x
–5 x + 47
( f − g )( x) =
9x – 2
( f − g )( x) =
D)
( f − g )( x) =
–5 x + 43
9x – 2
E)
( f − g )( x) =
–5 x + 5
8x – 2
–5 x 2 + 45 x – 10
9 x2 – 2 x
27. Use a graphing utility to graph the function and approximate (to two decimal places) any relative
minimum or relative maximum values.
f (x) = x3 + 3x2 + 2x + 3
A) relative maximum:
relative minimum:
B) relative maximum:
relative minimum:
C) relative maximum:
relative minimum:
D) relative maximum:
relative minimum:
E) relative maximum:
relative minimum:
(–1.58, 3.38)
(–0.42, 2.62)
(–0.42, 2.62)
(–1.58, 3.38)
(2.62, 46.63)
(3.38, 82.93)
(3.38, –1.58)
(2.62, –0.42)
(2.62, –0.42)
(3.38, –1.58)
28. Find the midpoint of the line segment joining the points.
(9, –2), (–9, 8)
A) (0, 3) B) (3, 0) C) (0, –3)
D) (9, –5)
E) (–5, 9)
29. Find the slope-intercept form of the equation of the line that passes through the given point and has the
indicated slope.
point: (–9, –8)
slope: m = 5
A) y = 5x – 9 B) y = 5x – 1 C) y = 5x + 31 D) y = 5x + 37
E) y = 5x – 8
30. Determine the quadrant(s) in which (x, y) is located so that the condition is satisfied.
xy > 0
A) quadrant IV
B) quadrants II and IV
C) quadrant I
D) quadrant III
E) quadrants I and III
31. Write the slope-intercept form of the equation of the line through the given point perpendicular to the
given line.
line: 8x – 40y = 6
1
11
1
1
A) y = –5x + 29 B) y = x –
C) y = 8x + 47 D) y = – x –
5
5
8
4
point: (6, –1)
E) y = –5 x +
32. Determine the intervals over which the function is increasing, decreasing, or constant.
A)
B)
C)
D)
E)
33. Find the zeroes of the functions algebraically.
x 2 – 7 x – 18
7x
x = 9, x = –2
f ( x) =
A)
B)
C)
1
x = –9, x = 2, x =
7
1
x=
7
D)
E)
x = –9, x = 2
x = 9, x = –2, x =
1
7
31
5
34. Describe the sequence of transformations from the related common function f ( x) = x to g.
g ( x) = − x + 8
A) reflection in the x-axis; then vertical shift 8 units down
B) reflection in the y-axis; then horizontal shift 8 units right
C) reflection in the y-axis; then vertical shift 8 units up
D) reflection in the y-axis; then horizontal shift 8 units left
E) reflection in the x-axis; then vertical shift 8 units up
35. Find g D f . when f (x) = x + 5
A) ( g D f )( x) = x2 + 10x + 25
B) ( g D f )( x) = x2 – 25
C)
g (x) = x2
D)
E)
( g D f )( x) = x2 + 5x + 25
( g D f )( x) = x2 + 25
( g D f )( x) = x2 + 5
36. Find the x- and y-intercepts of the graph of the equation y = x 4 – x 2 .
A) x-intercepts: ( –1, 0 ) , ( 0, 0 ) , (1, 0 ) ; y-intercept: ( 0, 0 )
B)
x-intercepts: ( 0, –1) , ( 0, 0 ) , ( 0,1) ; y-intercept: ( 0, 0 )
C) x-intercepts: ( –1, 0 ) , (1, 0 ) ; y-intercept: ( 0, 0 )
D) x-intercepts: ( –1, 0 ) , ( 0, 0 ) , (1, 0 ) ; y-intercepts: none
E)
37.
x-intercepts: ( 0, –1) , ( 0,1) ; y-intercept: ( 0, 0 )
2
2
3⎞ ⎛
5⎞ 9
⎛
Determine the center and radius of the circle represented by the equation ⎜ x + ⎟ + ⎜ y – ⎟ = .
4⎠ ⎝
2⎠
4
⎝
A)
D)
3
5⎞
9
⎛ 3 5⎞
⎛3
center: ⎜ – , ⎟ ; radius:
center: ⎜ , – ⎟ ; radius:
2⎠
2
4
⎝ 4 2⎠
⎝4
B)
E)
5⎞
3⎞
9
3
⎛3
⎛5
center: ⎜ , – ⎟ ; radius:
center: ⎜ , – ⎟ ; radius: –
4
2
2⎠
4⎠
⎝4
⎝2
C)
3
⎛ 5 3⎞
center: ⎜ – , ⎟ ; radius: –
2
⎝ 2 4⎠
38. The electrical resistance, R , of a wire is directly proportional to its length, l , and inversely
proportional to the square of its diameter, d . A wire 100 meters long of diameter 5 millimeters has a
resistance of 8 ohms. Find the resistance of a wire made of the same material that has a diameter of 1
millimeter and is 4 meters long.
A) R = 0.125 ohms
D) R = 10.5 ohms
B) R = 11.5 ohms
E) R = 8 ohms
C) R = 11.8 ohms
39. Write the standard form of the equation of the circle whose radius is 9 and whose center is the point
( 6,5) .
A)
B)
C)
( x + 6 ) + ( y + 5) = 81
2
2
( x – 6 ) + ( y – 5) = 9
2
2
( x – 5) + ( y – 6 ) = 9
2
2
D)
E)
( x – 5) + ( y – 6 ) = 81
2
2
( x – 6 ) + ( y – 5) = 81
2
2
40. Assuming that the graph shown has y-axis symmetry, sketch the complete graph.
A)
B)
C)
D)
E)
Answer Key
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
D
E
D
A
A
E
E
C
E
E
A
A
E
B
D
D
A
B
E
B
D
C
D
D
C
C
A
A
D
E
A
D
A
E
A
A
A
E
E
B