what are characteristics of the graph of the linear parent function?
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['Equation is y = x.', 'Domain and range are real numbers.', 'Slope, or rate of change, is constant.']
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When you are graphing inequalities, you will graph the ordinary linear functions just like we done before. The difference is that the solution to the inequality is not the drawn line but the area of the coordinate plane that satisfies the inequality. The boundary line is dashed for > and < and solid for ≥ and ≤.
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Answer: The second graph represents an odd function. The graph of an odd function will always be symmetric about the origin.
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['Zeros of linear functions: The blue line, y=12x+2 y = 1 2 x + 2 , has a zero at (−4,0) ; the red line, y=−x+5 y = − x + 5 , has a zero at (5,0) . ... ', 'Slope-intercept graph: Graph of the line y=−32x−2 y = − 3 2 x − 2 .']
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In mathematics, a parent function is the simplest function of a family of functions that preserves the definition (or shape) of the entire family. For example, for the family of quadratic functions having the general form.
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Linear functions are graphed as straight lines because the x variable is not raised to any exponent. They are like the flat bridge. Quadratic functions are typically in the form y = ax2 + bx + c. Quadratic functions will always have the x variable to the second power.
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Certain features of the graph of the common logarithmic function stay constant no matter how we alter a and b. The y-axis is always a vertical asymptote of the graph. The range of the graph is always (-∞, ∞). What are the characteristics of the graph of the natural logarithm y = a ln (bx)?
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Linear functions are those whose graph is a straight line. A linear function has the following form. y = f(x) = a + bx. A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.
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['Simple Line Graph: Only one line is plotted on the graph.', 'Multiple Line Graph: More than one line is plotted on the same set of axes. ... ', 'Compound Line Graph: If information can be subdivided into two or more types of data.']
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In the case of linear equations, the graph will always be a line. In contrast, a nonlinear equation may look like a parabola if it is of degree 2, a curvy x-shape if it is of degree 3, or any curvy variation thereof. While linear equations are always straight, nonlinear equations often feature curves.
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The graph of a quadratic function is called a parabola and has a curved shape. One of the main points of a parabola is its vertex. It is the highest or the lowest point on its graph. You can think of like an endpoint of a parabola.
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['Odd. End behavior go in different directions. If a function is positive, the left side of the graph will point down and the right side will point up (increasing from left to right). ... ', 'Straight line. Constant. Has a slope.']
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['(a) Objective function:', '(b) Constraints:', '(c) Non-negativity:', '(d) Linearity:', '(e) Finiteness:']
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Graphing the Absolute Value Function f (x) = | x| The graph looks like a "V", with its vertex at (0, 0). Its slope is m = 1 on the right side of the vertex, and m = - 1 on the left side of the vertex.
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The points at which the graph crosses or touches x- axis, give the real roots of the function (or zeros of the function) represented by the graph. If the graph touches x-axis and turns back, then it would be a double root at that point.
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A parent function is the simplest function of a family of functions. of this form is y = x2. The simplest parabola is y = x2, whose graph is shown at the right. The graph passes through the origin (0,0), and is contained in Quadrants I and II.
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Graphing the Absolute Value Function The graph of the absolute value function f (x) = | x| is similar to the graph of f (x) = x except that the "negative" half of the graph is reflected over the x-axis. Here is the graph of f (x) = | x|: f (x) = | x| The graph looks like a "V", with its vertex at (0, 0).