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  3. Chapter 3: Functions of two variables
  4. List of functions of two variables
  5. Polynomial functions
  6. Constant functions
  7. Exercise

Exercise

Which of the following functions is a constant function of two variables, and what is the function value in $(x,y)=(1,2)$?
$z(x,y) = 5$; the corresponding function value is 5.
$y(x) = 4$; the corresponding function value is 4.
$z(x,y) = 5$; the corresponding function value is $(1,2)$.
$z(x,y) = 5(x+y)$; the corresponding function value is 15.
Which of the following functions is a constant function of two variables, and what is the function value in $(x,y)=(1,2)$?
Antwoord 1 correct
Correct
Antwoord 2 optie
$y(x) = 4$; the corresponding function value is 4.
Antwoord 2 correct
Fout
Antwoord 3 optie
$z(x,y) = 5$; the corresponding function value is $(1,2)$.
Antwoord 3 correct
Fout
Antwoord 4 optie
$z(x,y) = 5(x+y)$; the corresponding function value is 15.
Antwoord 4 correct
Fout
Antwoord 1 optie
$z(x,y) = 5$; the corresponding function value is 5.
Antwoord 1 feedback
Correct: $z(x,y)=5$ is indeed a constant function of two variables. The function value is equal to 5 for every combination of $x$ and $y$, hence also for $(x,y)=(1,2)$.

Go on.
Antwoord 2 feedback
Wrong: $y(x)=4$ is a constant function of one variable, not of two.

See Constant functions of two variables.
Antwoord 3 feedback
Wrong: Although $z(x,y)=5$ is a constant function, the function value is the value of the output variable, not of the input variables.

See Functions of two variables.
Antwoord 4 feedback
Wrong: $z(1,2)=15$ is correct, but $z(x,y) = 5(x+y)$ is not a constant function.

See Constant functions of two variables.