Chapter 12.1, Exercise 7

Exercises 7-14, give the domain and range of the multivariable function.

\(f(x, y) = x^{2} + y^{2} + 2\)

\(0 \leq x^{2} + y^{2} + 2\)

\(-2 \leq x^{2} + y^{2}\)

\(x^{2} + y^{2} \geq -2\)

\(D:\{(x,y): x^{2} + y^{2} \geq -2\}\)

Domain: \(D:\{(x,y): x^{2} + y^{2} \geq -2\}\)

\(f(0,0): 0^{2} + 0^{2} + 2\)

\(f(0,0): 0 + 0 + 2\)

\(f(0,0): 2\)

\(R: \{(x,y): [2, \infty]\}\)

Range: \(R: \{(x,y): [2, \infty]\}\)

fun <- function(x, y) (x**2) + (y**2) + 2
xs <- seq(-250, 250, by=1)
ys <- c(0, 50, 100, 150, 200, 250, 300)
results <- mapply(fun, list(xs), ys)
colors <- c("pink", "red", "maroon", "black", "blue", "cyan", "skyblue")
matplot(xs, results, col=colors, type="l", lty=1, lwd=2, xlab="x", ylab="result")