função e equação do primeiro grau

[OrionRandD]

1. Esboce os gráficos das seguintes funções constantes:
   (a) f (x) = 1
   (b) f (x) = 3
   (c) f (x) = −2
   (d) f (x) = −5
   (e) f (x) = 4

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com octave:

f(x) = 1
x = linspace(0, 10, 100);
y = ones(size(x));
plot(x, y);

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f(x) = 3
x = linspace(0, 10, 100);
y = 3 * ones(size(x));
plot(x, y);

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f(x) = -2
x = linspace(0, 10, 100);
y = (-2) * ones(size(x));
plot(x, y);

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f(x) = -5
x = linspace(0, 10, 100);
y = (-5) * ones(size(x));
plot(x, y);

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f(x) = 4
x = linspace(0, 10, 100);
y = (4) * ones(size(x));
plot(x, y);

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2. Esboce no mesmo plano cartesiano os gráficos das seguintes funções lineares:

(a) f (x) = x and f (x) = 1
(b) f (x) = 2x and f (x) = 3
(c) f (x) = 3x and f (x) = -2
(d) f (x) = −x and f (x) = -5
(e) f (x) = −2x and f (x) = -4

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com octave:

f(x) = x
x = linspace(0, 10, 100);
y = x;
plot(x, y);

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f(x) = 1 and f(x) = x
x = linspace(0, 10, 100);
y1 = ones(size(x));
y2 = x;
plot(x, y1, x, y2);

;;;;;;;;;;;;;;;;;;;;;;;;;
f (x) = 2x
x = linspace(0, 10, 100);
y = 2 * x;
plot(x, y);

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f (x) = 2x and f (x) = 3
x = linspace(0, 10, 100);
y1 = 2 * x;
y2 = 3;
plot(x, y1, x, y2);

;;;;;;;;;;;;;;;;;;;;;;;;;
f (x) = 3x
x = linspace(0, 10, 100);
y = 3 * x;
plot(x, y);

;;;;;;;;;;;;;;;;;;;;;;;;;
f (x) = 3x and f (x) = -2
x = linspace(0, 10, 100);
y1 = 3 * x;
y2 = -2;
plot(x, y1, x, y2);

;;;;;;;;;;;;;;;;;;;;;;;;;
f (x) = −x
x = linspace(0, 10, 100);
y = -x;
plot(x, y);

;;;;;;;;;;;;;;;;;;;;;;;;;
f (x) = −x and f (x) = -5
x = linspace(0, 10, 100);
y1 = -x;
y2 = -5;
plot(x, y1, x, y2);

;;;;;;;;;;;;;;;;;;;;;;;;;
f (x) = −2x
x = linspace(0, 10, 100);
y = (-2) * x;
plot(x, y);

;;;;;;;;;;;;;;;;;;;;;;;;;
f (x) = −2x and f (x) = -4
x = linspace(0, 10, 100);
y1 = (-2) * x;
y2 = -4;
plot(x, y1, x, y2);

;;;;;;;;;;;;;;;;;;;;;;;;;
f (x) = x + 1
x = linspace(0, 10, 100);
y = x + 1;
plot(x, y);

;;;;;;;;;;;;;;;;;;;;;;;;;
(a) f (x) = x + 1

x = [1, 2, 3, 4, 5];
y = x + 1;

coefficients = polyfit(x, y, 1);
linear_coefficient = coefficients(1);
angular_coefficient = coefficients(2);
coefficients
linear_coefficient
angular_coefficient

;;;;;;;;;;;;;;;;;;;;;;;;;
(b) f (x) = 2x + 1

x = [1, 2, 3, 4, 5];
y = (2 * x) + 1;

coefficients = polyfit(x, y, 1);
linear_coefficient = coefficients(1);
angular_coefficient = coefficients(2);
coefficients
linear_coefficient
angular_coefficient

;;;;;;;;;;;;;;;;;;;;;;;;;

(c) f (x) = −x + 1

x = [1, 2, 3, 4, 5];
y = -x + 1;

coefficients = polyfit(x, y, 1);
linear_coefficient = coefficients(1);
angular_coefficient = coefficients(2);
coefficients
linear_coefficient
angular_coefficient

;;;;;;;;;;;;;;;;;;;;;;;;;

(d) f (x) = −x − 1

x = [1, 2, 3, 4, 5];
y = -x - 1;

coefficients = polyfit(x, y, 1);
linear_coefficient = coefficients(1);
angular_coefficient = coefficients(2);
coefficients
linear_coefficient
angular_coefficient

;;;;;;;;;;;;;;;;;;;;;;;;;

(e) f (x) = 5x − 5

x = [1, 2, 3, 4, 5];
y = (5 * x) - 5;

coefficients = polyfit(x, y, 1);
linear_coefficient = coefficients(1);
angular_coefficient = coefficients(2);
coefficients
linear_coefficient
angular_coefficient

;;;;;;;;;;;;;;;;;;;;;;;;;

(f) f (x) = −2x + 4

x = [1, 2, 3, 4, 5];
y = (-2 * x) + 4;

coefficients = polyfit(x, y, 1);
linear_coefficient = coefficients(1);
angular_coefficient = coefficients(2);
coefficients
linear_coefficient
angular_coefficient

;;;;;;;;;;;;;;;;;;;;;;;;;
(g) f (x) = 2x − 4

x = [1, 2, 3, 4, 5];
y = (2 * x) - 4;

coefficients = polyfit(x, y, 1);
linear_coefficient = coefficients(1);
angular_coefficient = coefficients(2);
coefficients
linear_coefficient
angular_coefficient

;;;;;;;;;;;;;;;;;;;;;;;;;

f = @(x) x + 1;
root = fzero(f, 0);
root

f = @(x) (2 * x) + 1;
root = fzero(f, 0);
root

f = @(x) -x + 1;
root = fzero(f, 0);
root

f = @(x) -x - 1;
root = fzero(f, 0);
root

f = @(x) (5 * x) - 5;
root = fzero(f, 0);
root

f = @(x) (-2 * x) + 4;
root = fzero(f, 0);
root

f = @(x) (2 * x) - 4;
root = fzero(f, 0);
root

Gráficos

f = @(x) x + 1;
ezplot(f, [-10, 10]);

f = @(x) (2 * x) + 1;
ezplot(f, [-10, 10]);

f = @(x) -x + 1;
ezplot(f, [-10, 10]);

f = @(x) -x - 1;
ezplot(f, [-10, 10]);

f = @(x) (5 * x) - 5;
ezplot(f, [-10, 10]);

f = @(x) (-2 * x) + 4;
ezplot(f, [-10, 10]);

f = @(x) (2 * x) - 4;
ezplot(f, [-10, 10]);

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Valor das funções

(a) f (x) = x + 1
x = 3;
result = x + 1

(b) f (x) = 2x + 1
x = 3;
result = (2 * x) + 1

(c) f (x) = −x + 1
x = 3;
result = −x + 1

(d) f (x) = −x − 1

x = 3;
result = −x −1

(e) f (x) = 5x − 5

x = 3;
result = (5 * x) - 5

(f) f (x) = −2x + 4

x = 3;
result = (-2 * x) + 4

(g) f (x) = 2x − 4
x = 3;
result = (2 * x) - 4