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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)=x2+y2;the corresponding function value is 10.
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).
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)=x2+y2;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)=x2+y2 is not a linear function.

See Linear functions of two variables.