Unit 1B Review
Functions, Direct and Inverse Variation, Solving Systems of Equations
1. Classify the following as a Direct Variation or an Inverse Variation,
A) D  4t
B) R 
9
t
C) F 
5
d
D) C 
S
24
2. For the Variations examples in number 1 above, identify the constant of variation (or
proportionality).
Solve Each system of non-linear equations by graphing.
3. −9 = −9√𝑥 + 8
4.
√16 − 2𝑥 = √2𝑥 − 4
5. √9𝑛 = 3
6.
x = √12 − 𝑥
8.
𝑥 2 + 𝑦 2 = 16
7.
6 + √5𝑥 − 34 = x
x – 2y = -4
Solve the following:
9. In an experiment, Joseph finds that amount of a chemical needed is directly related to the
time of its reaction with a certain catalyst. If he has 12 grams of the chemical and the reaction
1
time was second, what amount of chemical is needed to have a reaction that lasts 3 seconds?
2
10. The time it takes to fly from Los Angeles to New York varies inversely as the speed of the
plane. If the trip takes 6 hours at 900 km/h, how long would it take at 800 km/h?
11. Write a general variation formula for the following:
A) V varies directly with the square root of t.
B) F varies inversely with the sum of x and y.
C) The variable y varies directly with x and inversely with the square of z.
12. Find the Domain and Range of the following functions. Write them using interval notation.
a. h(x) = 2x – 1
b. g (x) = -𝒙𝟐 + 4
c. f(x) = (𝒙 − 𝟏)𝟑 + 1
Solve the following problems
13. The bending of a beam varies directly as its mass. A beam is bent 20mm by a mass of 40 kg. How
much will the beam bend with a mass of 100 kg?
14. In an electric circuit, the current varies inversely as the resistance. The current is 40 amps when the
resistance is 12 ohms. Find the current when the resistance is 20 ohms.
15. The length of the base of a triangle with constant area varies inversely as the height. When
the base is 18 cm long, the height is 7 cm. Find the length of the base when the height is 6 cm.
The following problems refer to the graphs on the final page of this review:
16. For each of the graphs in the next page find the following information. Where appropriate,
put the answers in interval notation.
a. Is it a function?
b. Find the Domain.
c. Find the Range.
d. Tell where the graph is decreasing.
e. Tell where the graph is increasing.
f. Find the relative minimum and/or maximum if possible.
g. Find the absolute minimum and/or maximum if possible.
h. Is the function even or odd or neither?
i. Describe the end behavior.