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This example shows how to define functions at the command line with anonymous functions.

Consider the function `10*x`

.

$$h(x)=10x$$

If we want to allow any multiplier of `x`

, not just 10, we might create a variable `g`

(where `g`

is initially set to 10), and create a new function

$$h(x)=g*x$$

Let's do this in MATLAB® by creating a function handle `h`

.

g = 10; h = @(x) g*x;

You can integrate the function by passing its handle to the `integral`

function.

integral(h,1,10)

ans = 495.0000

Consider another function:

$$f(x)=sin(\alpha x)$$

Create a function handle to this function where `alpha = 0.9`

.

alpha = 0.9; f = @(x) sin(alpha*x);

Plot the function and shade the area under it.

x = 0:pi/100:pi; area(x,f(x)); % You can evaluate f without feval title('f(x) = sin(\alpha x), \alpha =.9');

We can use the `integral`

function to calculate the area under the function between a range of values.

integral(f,0,pi)

ans = 2.1678

Consider the function:

$$f(x)=a{x}^{2}+bx+c$$

where `a = 1, b = -2, `

and` c = 1`

.

Create a function handle for it.

a = 1; b = -2; c = 1; f = @(x)(a*x.^2+b*x+c);

fplot(f); % Plot the function title('f(x)=ax^2+bx+c, a=1,b=-2,c=1'); hold on; % Find and plot the minimum minimum = fminbnd(f,-2,2); % We can pass the function handle directly % to the minimization routine plot(minimum,f(minimum),'d'); % We can evaluate the function without % using feval grid; hold off;

We can create handles to functions of many variables

```
a = pi;
b = 15;
f = @(x,y) (a*x+b*y);
fsurf(f);
title('f(x,y) = ax+by, a = \pi, b = 15');
```

We can also create handles to functions of functions

f = @(x) x.^2; g = @(x) 3*x; h = @(x) g(f(x)); h(3)

ans = 27