x f(x)
2.8 6.6
2.9 6.8
3 7
3.1 7.1
3.01 7.01
3.001 7.001
101234567
0
2
4
6
8
10
Ej.1: f(x) = {2x+1 si x 3 ; x+4 si x>3}
Ej.1: f(x) = {2x+1 si x 3 ; x+4 si x>3}
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A series of exercises focused on evaluating piecewise functions at specific points. Each example presents a different piecewise function defined over various intervals, along with a table of x and f(x) values to illustrate the function's behavior near the point of interest. These exercises are designed to help students understand how to apply the correct piece of the function based on the input value and to reinforce the concept of limits in the context of piecewise functions. 20 examples, each demonstrating a different piecewise function and its evaluation.
Typology: Lecture notes
2024/2025
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x f(x) 2.8 6. 2.9 6. 3 7 3.1 7. 3.01 7. 3.001 7. 1 0 1 2 3 4 5 6 7
Ej.1: f(x) = {2x+1 si x 3 ; x+4 si x>3}
Ej.1: f(x) = {2x+1 si x 3 ; x+4 si x>3}
x f(x) -1.2 -1. -1.1 -1. -1 - -0.9 0. -0.99 0. -0.999 0. 3 2 1 0 1 2 3
Ej.2: f(x) = {2x+1 si x -1 ; x^2 si x>-1}
Ej.2: f(x) = {2x+1 si x -1 ; x^2 si x>-1}
x f(x) 0.8 -0. 0.9 -0. 1 0 1.1 0. 1.01 0. 1.001 0. 1.0 0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.
Ej.4: f(x) = {x^2-1 si x 1 ; 2x-2 si x>1}
Ej.4: f(x) = {x^2-1 si x 1 ; 2x-2 si x>1}
x f(x)
Ej.5: f(x) = {-2x+5 si x 2 ; x-1 si x>2}
x f(x)
Ej.7: f(x) = {x^2+2 si x 0 ; 2 si x>0}
x f(x) 0.8 3. 0.9 3. 1 3 1.1 2. 1.01 2. 1.001 2. 1.0 0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.
Ej.8: f(x) = {-x^2+4 si x 1 ; -2x+5 si x>1}
Ej.8: f(x) = {-x^2+4 si x 1 ; -2x+5 si x>1}
x f(x)
Ej.10: f(x) = {2x-6 si x 3 ; x^2-9 si x>3}
x f(x) 0.8 1. 0.9 1. 1 1 1.1 1. 1.01 1. 1.001 1. 0.0 0.5 1.0 1.5 2.0 2.
Ej.11: f(x) = {-x+2 si x 1 ; x^2 si x>1}
Ej.11: f(x) = {-x+2 si x 1 ; x^2 si x>1}
x f(x) -3.2 0. -3.1 0. -3 1 -2.9 1. -2.99 1. -2.999 1. 4 3 2 1 0 1
Ej.13: f(x) = {sqrt(x+4) si x -3 ; x+4 si x>-3}
Ej.13: f(x) = {sqrt(x+4) si x -3 ; x+4 si x>-3}
x f(x) -0.2 0. -0.1 0. 0 1 0.1 1. 0.01 1. 0.001 1 2.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5 2.
Ej.14: f(x) = {2x+1 si x 0 ; x^2+1 si x>0}
Ej.14: f(x) = {2x+1 si x 0 ; x^2+1 si x>0}
x f(x) -1.2 -0. -1.1 -0. -1 0 -0.9 -0. -0.99 -0. -0.999 -0. 3.0 2.5 2.0 1.5 1.0 0.5 0.0 0.5 1.
Ej.16: f(x) = {3x+3 si x -1 ; -x-1 si x>-1}
Ej.16: f(x) = {3x+3 si x -1 ; -x-1 si x>-1}
x f(x) 3.8 4. 3.9 4. 4 5 4.1 5. 4.01 5. 4.001 5. 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.
Ej.17: f(x) = {x+1 si x 4 ; x^2-11 si x>4}
Ej.17: f(x) = {x+1 si x 4 ; x^2-11 si x>4}
x f(x)
Ej.19: f(x) = {x/2+2 si x -2 ; -x-1 si x>-2}
- 1.8 1. - 1.9 1. - 2.1 1. - 2.01 1. - 2.001 1. - 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.
- -0.2 2. - -0.1 2. - 0.1 - 0.01- 0.001
- 2.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5 2.
- 2.8 -0. - 2.9 -0. - 3.1 0. - 3.01 0. - 3.001 0.- 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.
- -2.2 0.
- -2.1 0.
- -2
- -1.9 0.
- -1.99 0.
- -1.999 0.
x f(x) 0.8 4 0.9 4 1 4 1.1 4. 1.01 4. 1.001 4. 1 0 1 2 3 4
Ej.20: f(x) = {4 si x 1 ; x+3 si x>1}
Ej.20: f(x) = {4 si x 1 ; x+3 si x>1}