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

Exercise

Which of the following functions is a linear function of two variables, and what is the function value in $(x,y)=(1,2)$?
$z(x,y) = -x + y$; the corresponding function value is 1.
$y(x) = 5x+2$; the corresponding function value is 7.
$z(x,y) = -x + y$; the corresponding function value is $(1,2)$.
$z(x,y) = x^2 + y^2$;the corresponding function value is 10.
Which of the following functions is a linear function of two variables, and what is the function value in $(x,y)=(1,2)$?
Antwoord 1 correct
Correct
Antwoord 2 optie
$y(x) = 5x+2$; the corresponding function value is 7.
Antwoord 2 correct
Fout
Antwoord 3 optie
$z(x,y) = -x + y$; the corresponding function value is $(1,2)$.
Antwoord 3 correct
Fout
Antwoord 4 optie
$z(x,y) = x^2 + y^2$;the corresponding function value is 10.
Antwoord 4 correct
Fout
Antwoord 1 optie
$z(x,y) = -x + y$; the corresponding function value is 1.
Antwoord 1 feedback
Correct: $z(x,y)=-x+y$ is indeed a linear function of two variables. The function value is $z(1,2)=-1+2=1$.

Go on.
Antwoord 2 feedback
Wrong: $y(x)=5x+2$ is a linear function of one variable, not of two.

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

See Functions of two variables.
Antwoord 4 feedback
Wrong: $z(1,2)=10$ is correct, but $z(x,y) = x^2 + y^2$ is not a linear function.

See Linear functions of two variables.