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Solution. The logarithmic function is defined only when the input is positive, so this function is defined when 5- 2x > 0 . Solving this inequality, 5 − 2x > 0 The input must be positive − 2x > − 5 Subtract 5 x < 5 2 Divide by -2 and switch the inequality. The domain of f(x) = log(5 − 2x) is (- ∞, 5 2).
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Graph the equation. y = − 2 ( x + 5) 2 + 4. This equation is in vertex form. y = a ( x − h) 2 + k. This form reveals the vertex, ( h, k) , which in our case is ( − 5, 4) . It also reveals whether the parabola opens up or down. Since a = − 2 , the parabola opens downward. This is enough to start sketching the graph.
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Figure 2.4.1. The graph of a constant function is a horizontal line. The domain consists of all real numbers ℝ and the range consists of the single value {c}. We next define the identity function44 f(x) = x. Evaluating any value for x will result in that same value. For example, f(0) = 0 and f(2) = 2.
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We'll use 0, 2, and 4 for the x -values. Plot the points and connect them, as shown in Figure 11.4.6 11.4. 6. This graph is a horizontal line passing through the y-axis at 4. A horizontal line is the graph of an equation that can be written in the form y = b. The line passes through the y-axis at (0, b).
2 Hoch 4
Algebra Graph y=e^ (-x) y = e−x y = e - x Exponential functions have a horizontal asymptote. The equation of the horizontal asymptote is y = 0 y = 0. Horizontal Asymptote: y = 0 y = 0
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To find the x -intercepts, we can solve the equation f ( x) = 0 . The x -intercepts of the graph of y = f ( x) are ( 2 3, 0) and ( − 2, 0) . Our work also shows that 2 3 is a zero of multiplicity 1 and − 2 is a zero of multiplicity 2 . This means that the graph will cross the x -axis at ( 2 3, 0) and touch the x -axis at ( − 2, 0) .
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What do you want to calculate? Calculate it! Example: y=2x+1 Example (Click to try) y=2x+1 How to graph your problem Graph your problem using the following steps: Type in your equation like y=2x+1 (If you have a second equation use a semicolon like y=2x+1 ; y=x+3) Press Calculate it to graph! Graphing Equations Video Lessons
Potenzfunktionen Einführung Matheretter
Anleitung Funktionsgraphen zeichnen Mathematik / Analysis - Plotter - Rechner 4.1 Funktionen: Hülle: Erster Graph: f (x) Ableitung Integral f -1 Von bis Term zeigen Zweiter Graph: g (x) Ableitung Integral g -1 Von bis Term zeigen Dritter Graph: h (x) Ableitung Integral h -1 Von bis Term zeigen Anzeigeeigenschaften: Bildtyp: Quadranten: Größe:
Potenzfunktionen Einführung Matheretter
Algebra Graph x=4 x = 4 x = 4 Since x = 4 x = 4 is a vertical line, there is no y-intercept and the slope is undefined. Slope: Undefined y-intercept: No y-intercept Find two points on the line. x y 4 0 4 1 x y 4 0 4 1 Graph the line using the slope, y-intercept, and two points. Slope: Undefined y-intercept: No y-intercept x y 4 0 4 1 x y 4 0 4 1
Potenzfunktionen Einführung Matheretter
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x = 4. and a second solution of the equation is (4, 0). We can now use the ordered pairs (0, 3) and (4, 0) to graph Equation (1). The graph is shown in Figure 7.6. Notice that the line crosses the x-axis at 4 and the y-axis at 3. For this reason, the number 4 is called the x-intercept of the graph, and the number 3 is called the y-intercept.
Gegeben ist die Funktion y=f(x)=0,5x^4 4x²3. Berechne Nullstelle, Hochpunkte, Tiefpunkte
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