Chapter P
Find the distance between (0, 0) and (6, 8).
10 units
What is the parent function of f(x) = |x| , and what shape does its graph make?
Absolute value function; V-shaped graph
What is the degree and leading coefficient of f(x) = −4x⁵ + 3x² − 7 ?
Degree 5; leading coefficient −4
What is 15% of 200?
30
What is the only even prime number?
2
Find the midpoint of the segment joining (−4, 6) and (8, −2).
(2,2)
If f(x) = 3x − 2 and g(x) = x² , find (f ∘ g)(2) .
10
Find the average rate of change of f(x) = x² + 1 from x = 1 to x = 4.
5
Evaluate mentally: 25² − 24² .
49
A clock reads 3:15. What is the smaller angle between its hour and minute hands?
7.5°
Write the equation of a circle with center (−3, 2) and radius 5.
(x + 3)² + (y − 2)² = 25
Describe the transformations of y = −2(x + 3)² + 5 from y = x² .
Left 3, reflect over x-axis, vertical stretch by 2, up 5
Find the remainder when f(x) = 2x³ − 3x² + x − 5 is divided by x − 2 .
1
If 2ˣ = 128 , what is x?
7
You roll two fair six-sided dice. What is the probability that their sum is exactly 7?
1/6
Solve for all complex solutions: x² + 4x + 13 = 0 .
x = −2 ± 3i
Find the inverse of f(x) = (2x − 5)/3 .
f⁻¹(x) = (3x + 5)/2
Find all real zeros of f(x) = x³ − 4x² − x + 4 .
x = −1, 1, 4
Simplify mentally: (3⁴ × 9²)/(27²) .
9
A bacteria population doubles every hour. If a container is full after 12 hours, when was it half full?
After 11 hours
A line passes through (−2, 5) and (4, −7). Write its equation in standard form.
2x + y = 1
Find the domain of h(x) = √(x + 2)/(x − 3) . Give your answer in interval notation.
[−2, 3) ∪ (3, ∞)
For f(x) = (2x² − 8)/(x² − x − 6) , identify any hole, vertical asymptote, and horizontal asymptote.
Hole at (−2, 8/5); vertical asymptote x = 3; horizontal asymptote y = 2
Without a calculator, find the exact value of 1 + 2 + 3 + ⋯ + 100.
5,050
Use n(n + 1)/2 = 100(101)/2 = 5,050.
Three consecutive positive integers have a product of 336. What are the integers?
6, 7, and 8