GRAPH FUNCTIONS
Domain and range of a function the domain is the set of all x coordinates of the points on the graph of the function, and the tour is the set of all coordinates in the y-axis The domain values \u200b\u200bare usually associated with the horizontal axis (x axis) and the values \u200b\u200bof travel with the vertical axis (the axis).
Example for discussion:
Determine the domain and path of the function f whose graph is:
Practice Exercise: Determine the domain and path following graph:
functions increasing, decreasing and constant
Definition: Let I be in range in the domain of a function f. Then:
1) f is increasing in the interval I if f (b)> f (a) provided that b> a in I.
2) f is decreasing on the interval I if f (b)
3) f is constant in the interval I if f (b) = f (a) for all b in I.
Examples:
1)
The function f (x) = 2x + 4 is an increasing function on real numbers.
2)
The function g (x) =-x3 is a decreasing in numbers real.
3)
GRAPH FUNCTIONS
Domain and range
The domain of a function is the set of all x coordinates of the points on the graph of the function, and the path is set of all coordinates in the y-axis The domain values \u200b\u200bare usually associated with the horizontal axis (x axis) and the values \u200b\u200bof travel with the vertical axis (the axis).
Example for discussion:
Determines the domain and path of the function f whose graph is:
Practice Exercise: Determine the domain and path following graph:
functions increasing, decreasing and constant
Definition : Let I be in range in the domain of a function f. Then:
1) f is increasing in the interval I if f (b)> f (a) provided that b> a in I.
2) f is decreasing on the interval I if f (b)
3) f is constant in the interval I if f (b) = f (a) for all b in I.
Examples:
1)
The function f (x) = 2x + 4 is an increasing function on real numbers.
2)
The function g (x) =-x3 is a decreasing function in the real numbers.
3)
The function h (x) = 2 is a function it counts in real numbers.
4)
The function f (x) = X2 is a decreasing function in the range from minus infinity to zero and increasing in the range of zero to infinity.
constant function
A constant function is a function of the form f (x) = b. Its graph is a horizontal line, the domain of the set of real numbers and route the set {b}.
Example:
The function f (x) = 2, the domain is the set of real numbers and the route is {2}. The slope (m) is zero.
Identity function
The identity function is the function of the form f (x) = x. The domain and path is the set of real numbers.
linear function
A linear function is a function of the form f (x) = mx + b, where m is different from zero, m and b are real numbers. The restriction m different from zero implies that the graph is a horizontal line. Neither its graph is a vertical line. The domain and path (range) of a function Linear is the set of real numbers.
Remember that if the slope (m) is positive the graph is increasing in real numbers and if the slope is negative the graph is decreasing in real numbers. The intercept is (0, b).
Example:
The function f (x) = 2x + 4, the slope is 2, so the graph is increasing in real numbers. The domain and path is the set of real numbers. The intercept is (0.4).
Exercise: Find the slope, the intercept, the x-intercept, domain and path of f (x) =-3x + 6. Then draw the graph.
Note: A function of the form f (x) = x is also a linear function but the intercept is zero. Its graph is a line that always passes through the origin.
Quadratic function A quadratic function is a function of the form f (x) = ax2 + bx + c, with a non-zero, where a, b and c are real numbers. The graph of a quadratic function is a parabola. If a> 0 then the parabola opens upward and if <0 entonces la parábola abre hacia abajo. El dominio de una función cuadrática es el conjunto de los números reales. El vértice de la parábola se determina por la fórmula:
f (x) = x2 is a quadratic function whose graph is a parabola that opens upward, since a> 0. The vertex is (0.0). The domain is the set of real numbers and the path is zero and positive real. The graph of a function that looks like f (x) = x2 is concave upward.
f (x) =-x2 is a quadratic function whose graph is a parabola that opens to down, because <0. El vértice es (0,0). El dominio es el conjunto de los números reales y el recorrido es el conjunto de los números reales negativos y el cero. La gráfica de una función que luce como f(x) = -x2 es cóncava hacia abajo.
Note: The axis of symmetry is x = h, where h is the abscissa of the vertex of the parabola, parallel to the axis of y.
Examples for discussion: Find the vertex, x intercepts, intercept, domain, path and axis of symmetry. Interval indicates that the function is increasing and decreasing. Draw the graph for each of the following functions:
1) f (x) = x2 - 2x - 3
2) g (x) =-x2 - 2x + 3
Practice Exercise: Let f (x) =-x2 + 4x - 4. Halla the vertex, x intercepts, intercept, domain and range. Interval indicates that the function is increasing and decreasing. Draw the graph.
absolute value function
The function is the absolute value of x. The domain is the set of real numbers and the path is zero and positive real numbers. Its graph is:
domain function
party domain match functions are functions that are formed by different equations for different parts of the domain. For example:
The graph of this function is:
The domain is the set of real numbers except zero, expressed as a range is (- ¥, 0) È (0, ¥). The journey is the set of real numbers except -1 and 1 and real numbers between -1 and 1, ie (- ¥, -1) E (1, ¥). The open points (0, -1) and (0.1) indicates that the points do not belong to the graph of f. Due to the separation of the graph at x = 0, we say that f is discontinuous at x = 0.
radical Function The function is the square root function. Its graph is as follows:
Its domain is [0, ¥) and travel is [0, ¥).
The function h (x) = 2 is a function it counts in real numbers.
4)
The function f (x) = x2 is a decreasing function in the range from minus infinity to zero and increasing in the range of zero to infinity.
constant function
A constant function is a function of the form f (x) = b. Its graph is a horizontal line, the domain of the set of real numbers and route the set {b}.
Example:
The function f (x) = 2, the domain is the set of real numbers and travel is {2}. The slope (m) is zero. Identity function
The identity function is the function of the form f (x) = x. The domain and path is the set of real numbers.
linear function
A linear function is a function of the form f (x) = mx + b, where m is different from zero, m and b are real numbers. The restriction m different from zero implies that the graph is a horizontal line. Neither its graph is a vertical line. The domain and path (range) of a linear function is the set of real numbers.
Remember that if the slope (m) is positive the graph is increasing in real numbers and if the slope is negative the graph is decreasing in real numbers. The intercept is (0, b).
Example:
The function f (x) = 2x + 4, the slope is 2, so the graph is increasing in real numbers. The domain and path is the set of real numbers. The intercept is (0.4).
Exercise: Find the slope, the intercept, the x-intercept, domain and path of f (x) =-3x + 6. Then draw the graph.
Note: A function of the form f (x) = x is also a linear function but the intercept is zero. Its graph is a line that always passes through the origin.
Quadratic function A quadratic function is a function of the form f (x) = ax2 + bx + c, with a non-zero, where a, b and c are real numbers. The graph of a quadratic function is a parabola. If a> 0 then the parabola opens upward and if <0 entonces la parábola abre hacia abajo. El dominio de una función cuadrática es el conjunto de los números reales. El vértice de la parábola se determina por la fórmula:
f (x) = x2 is a quadratic function whose graph is a parabola that opens upward, since a> 0. The vertex is (0.0). The domain is the set of real numbers and the path is zero and positive real. The graph of a function that looks like f (x) = x2 is concave upward.
f (x) =-x2 is a quadratic function whose graph is a parabola that opens downward, because <0. El vértice es (0,0). El dominio es el conjunto de los números reales y el recorrido es el conjunto de los números reales negativos y el cero. La gráfica de una función que luce como f(x) = -x2 es cóncava hacia abajo.
Note: The axis of symmetry is x = h, where h is the abscissa of the vertex parable, parallel to the axis of y.
Examples for discussion: Find the vertex, x intercepts, intercept, domain, path and axis of symmetry. Interval indicates that the function is increasing and decreasing. Draw the graph for each of the following functions:
1) f (x) = x2 - 2x - 3
2) g (x) =-x2 - 2x + 3
Practice Exercise: Let f (x) =-x2 + 4x - 4. Find the vertex, x intercepts, intercept, domain and range. Interval indicates that the function is increasing and decreasing. Draw the graph. Function
The absolute value function is the absolute value of x. The domain is the set of real numbers and the path is zero and positive real numbers. Its graph is:
domain function
party functions party domain are functions that are composed of different equations for different parts of the domain. For example:
The graph of this function is:
The domain is the set of real numbers except zero, expressed as interval is (- ¥, 0) E (0, ¥). The journey is the set of real numbers except -1 and 1 and real numbers between -1 and 1, ie (- ¥, -1) E (1, ¥). The open points (0, -1) and (0.1) indicates that the points do not belong to the graph of f. Due to the separation of the graph at x = 0, we say that f is discontinuous at x = 0. Radical function
The function is the square root function. Its graph is as follows:
Its domain is [0, ¥) and travel is [0, ¥).
0 comments:
Post a Comment