Section 1.6
Question 1. Describe all numbers x that are at a distance of 1
2
from the number 4. Express
this using absolute value notation.
Question 2. Find all function values f(x) such that the distance from f(x) to the value 8
is less than 0.03 units. Express this using absolute value notation.
Question 3. Solve the following equation:
|5x − 2| = 11
Question 4. Solve the following equation:
3 |x + 1| − 4 = 5
Question 5. Solve the following inequality. Moreover, write your answer 1) in interval
notation, and 2) as a compound inequality, if possible:
2 |v − 7| − 4 ≥ 42
Question 6. Solve the following inequality. Moreover, write your answer 1) in interval
notation, and 2) as a compound inequality, if possible:
|3x − 5| ≥ 13
1
2
Question 7. Solve the following inequality. Moreover, write your answer 1) in interval
notation, and 2) as a compound inequality, if possible:
|3x − 5| ≥ −13
Question 8. If possible, find all values of a such that there are no x−intercepts for:
f(x) = 2|x + 1| + a
Question 9. Students who score within 18 points of the number 82 will pass a particular
test. Write this statement using absolute value notation and use the variable x for the score.
Section 1.7
Question 10. Can a function be its own inverse? Explain why not or give an example.
Question 11. Are one-to-one functions either always increasing or always decreasing? Why
or why not?
Question 12. Find f
−1
(x) when:
f(x) = x
x + 2
Question 13. Find a domain on which the following function function is both one-to-one
and non-decreasing. Write the domain in interval notation. Then find the inverse of the
function restricted to that domain.
f(x) = (x − 6)2
3
Question 14. A function f(x) is given on the graph below. Sketch a graph of f
−1
(x).
Question 15. Using the same graph and function from question 14, find
(a) f(6)
(b) f
−1
(2)
Question 16. To convert from x degrees Celsius to y degrees Fahrenheit, we use the formula
f(x) = 9
5
x + 32. Find the inverse function, if it exists, and explain its meaning.
Question 17. The circumference C of a circle is a function of its radius given by C(r) = 2πr.
Express the radius of a circle as a function of its circumference. Call this function r(C). Find
r(36π) and interpret its meaning.
Question 18. A car travels at a constant speed of 50 miles per hour. The distance the
car travels in miles is a function of time, t, in hours given by d(t) = 50t. Find the inverse
function by expressing the time of travel in terms of the distance traveled. Call this function
t(d). Find t(180) and interpret its meaning.