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 yy depends on xx, then knowing xx uniquely determines yy.

Temperature determines ice cream sales—sales DEPEND ON temperature.

Showing a random 20 of 50 problems.

Example 1

medium
Is yy a function of xx given by the graph y=∣x∣y = |x|?

Example 2

challenge
Determine all values of kk for which y=kx2+(k−1)x+1y = kx^2 + (k-1)x + 1 makes yy depend on xx as a genuine quadratic (not linear/constant), and find y(1)y(1) in terms of kk.

Example 3

medium
Does the graph of a circle x2+y2=4x^2 + y^2 = 4 pass the vertical line test?

Example 4

medium
If yy is a function of xx and also xx is a function of yy, what term describes this stronger condition?

Example 5

easy
In {(1,2),(1,5),(3,6)}\{(1,2),(1,5),(3,6)\}, is yy a function of xx?

Example 6

hard
What is the range of f(x)=x2f(x) = x^2 over all real xx?

Example 7

easy
If h(x)=5h(x) = 5 for every real xx, is hh a function?

Example 8

medium
Is yy functionally dependent on xx in x2+y2=25x^2 + y^2 = 25?

Example 9

easy
Is {(2,5),(3,5),(4,5)}\{(2,5),(3,5),(4,5)\} a function?

Example 10

medium
For f(x)=4−xf(x) = \sqrt{4 - x}, find the domain.

Example 11

easy
What is the domain of the relation {(1,4),(2,5),(3,6)}\{(1,4),(2,5),(3,6)\}?

Example 12

easy
In {(1,2),(2,4),(3,6)}\{(1,2),(2,4),(3,6)\}, is yy a function of xx?

Example 13

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

Example 14

easy
Is {(0,1),(0,−1)}\{(0,1),(0,-1)\} a function?

Example 15

medium
Does the equation x2+y2=25x^2 + y^2 = 25 define yy as a function of xx?

Example 16

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