Practice Functional Dependency in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

A relationship where the value of one quantity (the output or dependent variable) is completely determined by the value of another quantity (the input or independent variable). If $y$ depends on $x$ , then knowing $x$ uniquely determines $y$ .

Temperature determines ice cream sales—sales DEPEND ON temperature.

Showing a random 20 of 50 problems.

Example 1

medium

y

a function of

x

given by the graph

y = |x|

Example 2

challenge

Determine all values of

k

for which

y = kx^2 + (k-1)x + 1

makes

y

depend on

x

as a genuine quadratic (not linear/constant), and find

y(1)

in terms of

k

Example 3

medium

Does the graph of a circle

x^2 + y^2 = 4

pass the vertical line test?

Example 4

medium

y

is a function of

x

and also

x

is a function of

y

, what term describes this stronger condition?

Example 5

easy

\{(1,2),(1,5),(3,6)\}

, is

y

a function of

x

Example 6

hard

What is the range of

f(x) = x^2

over all real

x

Example 7

easy

h(x) = 5

for every real

x

, is

h

a function?

Example 8

medium

y

functionally dependent on

x

x^2 + y^2 = 25

Example 9

easy

\{(2,5),(3,5),(4,5)\}

a function?

Example 10

medium

For

f(x) = \sqrt{4 - x}

, find the domain.

Example 11

easy

What is the domain of the relation

\{(1,4),(2,5),(3,6)\}

Example 12

easy

\{(1,2),(2,4),(3,6)\}

, is

y

a function of

x

Example 13

medium

Is birth month a function of birth date (year-month-day)?

Example 14

easy

\{(0,1),(0,-1)\}

a function?

Example 15

medium

Does the equation

x^2 + y^2 = 25

define

y

as a function of

x

Example 16

easy

Does

\{(1,2), (1,3), (2,4)\}

represent a function?

Example 17

medium

A table lists 30 students by name with their birth month. Is birth month a function of name?

Example 18

hard

A weather model: temperature depends on time of day. Suppose at 3 PM the temperature is recorded as both 71°F and 73°F by two thermometers. Is temperature a function of time here?

Example 19

easy

Which is the independent variable in 'ice cream sales depend on temperature'?

Example 20

easy

Correlation vs dependency: shoe size and reading ability both rise with age in children. Does shoe size functionally determine reading ability?

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Related Concepts

Function Variables Function Families Causation