Cumulative Exam — Cumulative exam Answers

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According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function?f(x) = (x3 – 3x + 1)2

A
2 roots
B
3 roots
C
6 roots
D
9 roots
42
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Which graph represents the function ?

Question illustration
A
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve down and to the left in quadrants 3 and 4.
Option A
B
On a coordinate plane, a hyperbola is shown. One curve opens up and to the left in quadrant 2, and the other curve opens down and to the right in quadrants 3, 4, and 1.
Option B
C
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve down and to the left in quadrants 2, 1, and 4.
Option C
D
On a coordinate plane, a hyperbola is shown. One curve opens up and to the left in quadrant 2, and the other curve opens down and to the right in quadrants 4 and 1.
Option D
43

The parent function f(x) = x3 is translated to form g(x), as shown on the graph. The translated function can be written in the form g(x) = (x – h)3 + k.

Question illustration
A
h = 4 k = –2
B
h = –4 k = –2
C
h = 4 k = 2
D
h = –4 k = 2
44

Which graph represents ?

Question illustration
A
On a coordinate plane, a parabola with a vertex at (0, 0) opens up.
Option A
B
On a coordinate plane, a curve that begins at (0, 0) opens down and to the right in quadrant 1.
Option B
C
On a coordinate plane, a cubic function is vertical and goes through (0, 0).
Option C
D
On a coordinate plane, a cubic function is horizontal and goes through (0, 0).
Option D
45

Consider the graph of f(x) = 5x 6 – 5x 5 – x 4.

Question illustration
A
One-half minus StartFraction 3 Over 10 EndFraction StartRoot 5 EndRoot less-than x less-than one-half + StartFraction 3 Over 10 EndFraction StartRoot 5 EndRoot
Option A
B
One-half minus StartFraction 3 Over 10 EndFraction StartRoot 5 EndRoot less-than-or-equal-to x less-than-or-equal-to one-half + StartFraction 3 Over 10 EndFraction StartRoot 5 EndRoot
Option B
C
x less-than one-half minus StartFraction 3 Over 10 EndFraction StartRoot 5 EndRoot and x greater-than one-half + StartFraction 3 Over 10 EndFraction StartRoot 5 EndRoot
Option C
D
x less-than-or-equal-to one-half minus StartFraction 3 Over 10 EndFraction StartRoot 5 EndRoot and x greater-than-or-equal-to one-half + StartFraction 3 Over 10 EndFraction StartRoot 5 EndRoot
Option D
46

What is the solution of ?

Question illustration
A
–8
B
–6
C
8
D
9
47

What is the value of ?

Question illustration
A
–4.00
B
–0.25
C
1.51
D
2.41
48

Juan jogs each day from his house to a local park, and then he jogs back along the same route. On his way to the park, he averages 4 miles per hour. On his way home, he averages 6 miles per hour. If the total trip takes hours, which equation can be used to find x, the distance in miles from Juan’s house to the park? Distance (mi)Rate (mi/hr)Time (hr)Trip to Parkx4 mph Trip to Homex6 mph

Question illustration
A
StartFraction x Over 4 EndFraction + StartFraction x Over 6 EndFraction = 1
Option A
B
StartFraction x Over 4 EndFraction + StartFraction x Over 6 EndFraction = 1 and one-half
Option B
C
4 x + 6 x = 1 and one-half
Option C
D
4 x + 6 x = 1
Option D
49

What is the solution of ?

Question illustration
A
x = –2500
B
x = –50
C
x = –2.5
D
no solution
50

What is the solution of ?

Question illustration
A
x = 5
B
x = 13
C
x = 20
D
x = 328

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