options(scipen = 7)
ì˜ˆì œ 2-1.
x <- seq(-2, 3, by = 0.01)
y <- 3*x^4 - 4 * x^3 - 12 * x^2 + 5
plot(x, y, type ="l", yaxt = "n")
abline(h = 0, v = 0, lty = 3)
axis(side = 2, at = c(-27, 0, 5), labels = c(-27, 0, 5))
abline(h = c(-27, 5), lty = 2)
ì˜ˆì œ 2-5.
x <- seq(-30, 30, by = 0.01)
y <- sign(x) * (abs(x))^(1/3)
plot(x, y, type = "l", xaxt = "n")
abline(h = 0, v = 0, lty = 3)
axis(side = 1, at = c(-27, 0, 27), labels = c(-27, 0, 27))
abline(h = c(-3, 3), v = c(-27, 27), lty = 2)
ì˜ˆì œ 7.
x <- seq(-1.5, 4.5, by = 0.01)
y <- x^4 - 4 * x^3
plot(x, y, type = "l", xaxt = "n", yaxt = "n")
abline(h = 0, v = 0, lty = 3)
axis(side = 1, at = c(0, 2, 3, 4), labels = c(0, 2, 3, 4))
axis(side = 2, at = c(0, -16, -27, 0), labels = c(0, -16, -27, 0))
points(x = c(0, 2, 3, 4), y = c(0, -16, -27, 0), pch = 21, col = "black", bg = "white")
ì˜ˆì œ 3-1.
x <- seq(-2, 2, by = 0.01)
y <- 1/(x^2 - 1)
plot(x, y, type = "l", ylim = c(-20, 20))
abline(h = 0, v = 0, lty = 3)
abline(v = c(-1, 1), lty = 2)
axis(side = 2, at = -1, labels = -1, las = 1)
abline(h = -1, lty = 2)
ì˜ˆì œ 3-2
x <- seq(-20, 20, by = 0.01)
y <- (x^2 - 1)/(x^2 + 1)
plot(x, y, type = "l")
abline(h = 0, v = 0, lty = 3)
abline(h = 1, lty = 2)
ì˜ˆì œ 3-3
x <- seq(-20, 20, by = 0.01)
y <- (3*x^2 - x - 2)/(5*x^2 + 4*x + 1)
plot(x, y, type = "l")
abline(h = 0, v = 0, lty = 3)
abline(h = 0.6, lty = 2)
x <- seq(-2, 1, by = 0.01)
y <- (3*x^2 - x - 2)/(5*x^2 + 4*x + 1)
plot(x, y, type = "l")
abline(h = 0, v = 0, lty = 3)
abline(h = 0.6, lty = 2)
x <- seq(-2, 1, by = 0.01)
y <- (3*x^2 - x - 2)/(5*x^2 + 4*x + 1)
f.3.3 <- function(x){
(3*x^2 - x - 2)/(5*x^2 + 4*x + 1)
}
f.3.3(c((-13 - 5*sqrt(2))/17, (-13 + 5*sqrt(2))/17))
## [1] 1.035534 -6.035534
plot(x, y, type = "l", xaxt = "n")
abline(h = 0, v = 0, lty = 3)
abline(h = 0.6, lty = 2)
axis(side = 1, at = c((-13 - 5*sqrt(2))/17, (-13 + 5*sqrt(2))/17), labels = c("alpha", "beta"))
x <- seq(-1, 3, by = 0.01)
y <- (sqrt(2*x^2 + 1))/(3*x - 5)
#f.3.4 <- function(x){
# (sqrt(2*x^2 + 1))/(3*x - 5)
# }
#f.3.4(c((-13 - 5*sqrt(2))/17, (-13 + 5*sqrt(2))/17))
plot(x, y, type = "l", ylim = c(-3, 5))
abline(h = 0, v = 0, lty = 3)
abline(h = c(-sqrt(2)/3, sqrt(2)/3), v = 5/3, lty = 2)
