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3.3 Piecewise Functions . 1. Use the piecewise function to evaluate the following. 𝑓(𝑥) = 3 𝑥−2, 𝑥< −3 2𝑥. 2. −3𝑥, −3 < 𝑥≤6 8, 1 𝑥> 6. 2. Graph the following piecewise function. 𝑓(𝑥) = − 1 3 𝑥−2, 𝑥≤0 2 𝑥+ 1, 𝑥> 0
Piecewise Functions WS. Evaluate the function for the given value of x. Match the piecewise function with its graph. Carefully graph each of the following. Identify whether or not he graph is a function. Then, evaluate the graph at any specified domain value.
20 sty 2022 · Graph each formula of the piecewise function over its corresponding domain. Use the same scale for the x-axis and y-axis for each graph. Indicate inclusive endpoints with a solid circle and exclusive endpoints with an open circle.
Evaluating Piecewise Functions. Evaluate and find each function value. 1. f(x) = + 1 3x – 2. < 1. ≥ 1. 2. f(x) = Find: f(1) f(–2) f(3) 3. f(x) = x + 4 | 4x + 1. ≤ 0. > 0 Find: f(–4) f(–2) f(3) 4. f(x) = Find: f(–5) f(0) f(5) Find: x – 3 5x2. 2x – 6 x3. f(–3/2) f(–1) f(1/2) 5. f(x) = 2| x |. (x + 1)2. + 2. < –3 –3 ≤ x < 4. ≥ 4. 6. f(x) = Find: f(–4)
Find a piecewise function to calculate the total tax T(x) on an income of x dollars. Solution. For x 10;000 the rate is .1, so T(x) = :1x on this interval. For 10;000 < x 25;000; the rate is .15. Similar to the previous example, we need to nd a point. When x = 10;000; then y = :1 10;000 = 1;000: Now using point-slope form,
A piecewise function is a function defi ned by two or more equations. Each “piece” of the function applies to a different part of its domain. An example is shown below. f(x) = { x − 2, 2x + 1, if x ≤ 0 if x > 0 The expression x − 2 represents the value of f when x is less than or equal to 0. The expression 2x + 1 represents the value ...
You have a summer job that pays time and half for overtime. That means, if you work more than 40 hours in a week, your hourly wage for the extra hours in 1.5 times your normal rate of $7 per hour. Write a piecewise function describing your weekly pay, P in term of the number of hours worked, h.
