The document discusses several types of functions:
1) Linear functions have an expression that is a polynomial of first degree and their graph is a straight line. Examples are given.
2) Quadratic functions contain terms of up to second degree and their graph is a parabola. They can have one or multiple variables.
3) Cubic functions are polynomial functions of third degree with the form f(x)=ax3+bx2+cx+d. Their derivative is quadratic and integral is quartic.
4) Reciprocal or inverse functions satisfy the property that if f(x)=y then f-1(y)=x, undoing the mapping of the original function.
5) Ex
It is a powerpoint presentation that will help the students to enrich their knowledge about Senior High School subject of General Mathematics. It is comprised about Rational functions and its zeroes. It is also comprised of some examples and exercises to be done for the said topic.
It is a powerpoint presentation that will help the students to enrich their knowledge about Senior High School subject of General Mathematics. It is comprised about Rational functions and its zeroes. It is also comprised of some examples and exercises to be done for the said topic.
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2. FUNCIÓN LINEAL
Una función lineal es una función cuyo dominio
son todos los números reales, cuyo codominio
también todos los números reales, y cuya
expresión analítica es un polinomio de primer
grado.
La función lineal se define por la ecuación f(x) = mx + b ó y = mx
+ b llamada ecuación canónica, en donde m es la pendiente de
la recta y b es el intercepto con el eje Y.
Por ejemplo, son funciones lineales f(x) = 3x + 2 g(x) = - x + 7
h(x) = 4 (en esta m = 0 por lo que 0x no se pone en la ecuación)
Esta función es una regla de correspondencia que dice lo
siguiente: "A cada número en el dominio de f se le relaciona con
el cuadrado de ese número mas el triple de ese número menos
seis". Otra manera de ver esto es escribiendo la función de la
siguiente manera: 𝑥 = f ( ) = ( )2 + 3( ) − 6
3. FUNCIÓN
CUADRÁTICA
En álgebra, una función cuadrática, un
polinomio cuadrático, o un polinomio de grado 2,
es una función polinómica con una o más
variables en la que el término de grado más alto
es de segundo grado. Por ejemplo, una función
cuadrática en tres variables x, y, y z contiene
exclusivamente los términos x2, y2, z2, xy, xz,
yz, x, y, z, y una constante:
con al menos uno de los coeficientes a, b, c, d,
e o f de los términos de segundo grado que no
son cero.
Una función cuadrática univariada (variable
única) tiene la forma1con una sola variable, en
este caso x. La gráfica de una función
cuadrática univariada es una parábola cuyo eje
de simetría es paralelo al eje y, como se
muestra a la derecha.
Si la función cuadrática se establece igual a
cero, entonces el resultado es una ecuación
cuadrática. Las soluciones a la ecuación
univariable se denominan raíces de la función
univariable.
El caso bivariable en términos de las variables x
e y tiene la formacon al menos uno de los
coeficientes a, b o c no iguales a cero. Una
ecuación que establece esta función igual a
cero da lugar a una sección cónica (una
circunferencia u otra elipse, una parábola o una
hipérbola).
En general, puede haber un número
arbitrariamente grande de variables, en cuyo
caso la superficie resultante se llama cuadrática,
pero el término de grado más alto debe ser de
grado 2, como x2, xy, yz, etc.
La forma general de una función
cuadrática es f ( x ) = ax 2 + bx + c . La
gráfica de una función cuadrática es
una parábola , un tipo de curva de 2
dimensiones.
4. FUNCIÓN CÚBICA
La función cúbica es una función
polinómica de tercer grado. Se escribe de
la siguiente manera:
f(x)=ax^{3}+bx^{2}+cx+d,}
f(x) = ax^3 + bx^2 + cx + d ,}
donde los coeficientes son números
racionales y siempre a es distinto de 0.
Tanto el dominio de definición como el
conjunto imagen de estas funciones tienen
como elementos a los números reales.
La derivada de una función cúbica es una
función cuadrática y su integral, una
función cuártica.
5. FUNCIÓN RECIPROCA
La función reciproca o inversa de f es otra
función f−1 que cumple que:
especialmente en análisis matemático, si f es
una función que asigna elementos de I en
elementos de J, en ciertas condiciones será
posible definir la función f -1 que realice el
camino de vuelta de J a I. En ese caso diremos
que f -1 es la función inversa de f.
El dominio de f−1 es el recorrido de f.
El recorrido de f−1 es el dominio de f.
Si queremos hallar el recorrido o rango de una función tenemos que hallar el
dominio de su función inversa.
Si dos funciones son reciprocas su composición es la función identidad.
(f o f −1) (x) = (f −1 o f) (x) = x
Las gráficas de f y f -1 son simétricas respecto de la bisectriz del primer y tercer
cuadrante.
6. FUNCIÓN
EXPONENCIAL
Las funciones exponenciales tienen la forma
f(x) = bx, donde b > 0 y b ≠ 1. Al igual que
cualquier expresión exponencial, b se llama
base y x se llama exponente. ... Con la
definición f(x) = bx y las restricciones de b > 0 y
b ≠ 1, el dominio de la función exponencial es
el conjunto de todos los números reales. Función Exponencial Se conoce como función
exponencial a la función f de variable real cuya
regla de correspondencia es: Si a > 0; a ≠ 1; x €
IR.
.