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基础函数绘制

R语言可通过curve()函数直接绘制数学函数图形，无需预先生成数据点。例如绘制正弦函数：

curve(sin, from = -pi, to = pi, col = "blue", lwd = 2)

自定义函数绘制

对于用户自定义函数，需先定义函数表达式：

my_function <- function(x) x^2 + 2*x + 1
curve(my_function, from = -5, to 5, n = 1000)

多函数叠加绘制

使用add = TRUE参数可在同一图形上叠加多个函数：

curve(sin, -pi, pi, col = "red")
curve(cos, -pi, pi, col = "blue", add = TRUE)

参数化函数绘制

处理含参数的函数时，可通过匿名函数传递参数：

a <- 2
curve(function(x) a*sin(x), 0, 2*pi)

离散点绘制法

对于无法用表达式表示的函数，可生成离散点后绘图：

x <- seq(-3, 3, length.out = 100)
y <- dnorm(x)  # 标准正态分布密度函数
plot(x, y, type = "l")

图形定制技巧

通过图形参数增强可视化效果：

curve(exp, -2, 2, main = "Exponential Function",xlab = "Input", ylab = "Output",col = "darkgreen", lty = 2)
grid()  # 添加网格线

特殊函数绘制

统计分布函数可直接调用：

curve(dnorm, -3, 3)  # 正态分布密度
curve(pnorm, -3, 3)  # 正态分布累积概率

# 设置随机种子
set.seed(123)# 定义x值范围
x <- seq(-10, 10, length.out = 200)# 设置图形布局为3行4列
par(mfrow = c(2, 2), mar = c(4, 4, 2, 2))  # 调整边距# 1. 线性函数
y1 <- 2 + 0.5 * x
plot(x, y1, type = "l", col = "blue", lwd = 2, main = "Linear Function", xlab = "x", ylab = "y")# 2. 多项式函数
y2 <- 2 + 0.5 * x + 0.1 * x^2
plot(x, y2, type = "l", col = "red", lwd = 2, main = "Polynomial Function", xlab = "x", ylab = "y")# 3. 指数函数
y3 <- 2 * exp(0.3 * x)
plot(x, y3, type = "l", col = "green", lwd = 2, main = "Exponential Function", xlab = "x", ylab = "y")# 4. 对数函数
y4 <- 2 + 0.5 * log(abs(x) + 1)  # 避免对负数取对数
plot(x, y4, type = "l", col = "purple", lwd = 2, main = "Logarithmic Function", xlab = "x", ylab = "y")# 设置图形布局为3行4列
par(mfrow = c(2, 2), mar = c(4, 4, 2, 2))  # 调整边距# 5. 幂函数
y5 <- 2 * x^0.5
plot(x, y5, type = "l", col = "orange", lwd = 2, main = "Power Function", xlab = "x", ylab = "y")# 6. 逻辑函数
y6 <- 1 / (1 + exp(-(2 + 0.5 * x)))
plot(x, y6, type = "l", col = "brown", lwd = 2, main = "Logistic Function", xlab = "x", ylab = "y")# 7. 正弦函数
y7 <- 2 * sin(0.5 * x + 1)
plot(x, y7, type = "l", col = "pink", lwd = 2, main = "Sine Function", xlab = "x", ylab = "y")# 8. 余弦函数
y8 <- 2 * cos(0.5 * x + 1)
plot(x, y8, type = "l", col = "cyan", lwd = 2, main = "Cosine Function", xlab = "x", ylab = "y")# 设置图形布局为3行4列
par(mfrow = c(2, 2), mar = c(4, 4, 2, 2))  # 调整边距# 9. 高斯函数
y9 <- 2 * exp(-((x - 0)^2) / (2 * 1^2))
plot(x, y9, type = "l", col = "magenta", lwd = 2, main = "Gaussian Function", xlab = "x", ylab = "y")# 10. 双曲函数
y10 <- 2 * tanh(0.5 * x + 1)
plot(x, y10, type = "l", col = "gray", lwd = 2, main = "Hyperbolic Function", xlab = "x", ylab = "y")# 11. 双指数函数y11 <- 2 * exp(-0.5 * abs(x))
plot(x, y11, type = "l", col = "gray", lwd = 2, main = "Hyperbolic Function", xlab = "x", ylab = "y")# 12. 三次多项式函数y12 <- 2 + 0.5 * x + 0.1 * x^2 + 0.01 * x^3
plot(x, y12, type = "l", col = "gray", lwd = 2, main = "Hyperbolic Function", xlab = "x", ylab = "y")