Math1000 section2.2
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This document discusses graphing functions. It begins by introducing common functions like linear, quadratic, cubic, rational, absolute value, square root, and cube root functions. Examples of their graphs are shown. It then discusses using the vertical line test to determine if something is a function. Piecewise functions are introduced next along with steps for graphing them which include graphing each piece and indicating open and closed points. Examples of piecewise functions are given and discussed. The document concludes by noting T-tables can be used to graph but plotting each piece of piecewise functions is more accurate.
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College algebra in context 5th edition harshbarger solutions manual
The document discusses solutions to exercises from a College Algebra textbook. It provides the steps to solve 16 different math equations involving variables like x and t. The equations use concepts like linear models, properties of equality, and combining like terms. Solutions are found by applying division, multiplication, addition or subtraction properties, or graphing the equations to find the intersection point of the lines.
Taller parcial 2
APLICACIONES DE ESPACIOS Y
SUBESPACIOS VECTORIALES EN LA
CARRERA DE INGENIERA EN TECNOLOGIAS
DE LA INFORMACION.
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This document contains an activity sheet for a Calculus with Analytic Geometry course. It includes multiple problems involving graphing points and lines, finding distances, slopes, equations of circles, parabolas, and hyperbolas, as well as limits, functions, continuity, and differentiation. The activity sheet provides spaces for students to show their work and solutions.
graphs of functions 2
Here are the steps to solve this problem:
1) The given equation is: y = x2 + 2x
2) To complete the table, we need to calculate the value of y when x = -3 and when x = 1
3) When x = -3:
y = (-3)2 + 2(-3)
y = 9 - 6
y = 3
4) When x = 1:
y = 12 + 2(1)
y = 1 + 2
y = 3
So the completed table is:
Table 1
x -3 1
y 3 3
(b) Sketch the graph of y = x2 + 2
How to graph Functions
This lesson discusses graphing functions. It begins with examples of graphing functions given a limited domain by finding ordered pairs that satisfy the function and plotting the points. It then covers graphing functions with a domain of all real numbers by choosing values of x, finding corresponding y-values, plotting points to see a pattern, and drawing a line with arrowheads. The lesson shows how to use graphs to find function values and solve real-world problems by limiting domains to non-negative values.
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Chapter 2
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2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
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4. BCP, Surveying volume 1
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Math1000 section2.2
- 1. Math 1000 Stuart Jones Section2.2 Graphs of Functions
- 2. Math 1000 Stuart Jones This section begins our focus over the next several sections of graphing. We are going to skip the basic graphing technique using T-tables, as it is assumed everyone knows how to graph using a T-table. We will then begin our study of graphs with the common graphs you need to know.
- 3. Math 1000 Stuart Jones Linear Function: y = x −5 −4 −3 −2 −1 1 2 3 4 5 −5 −4 −3 −2 −1 1 2 3 4 5
- 4. Math 1000 Stuart Jones Quadratic Function: y = x2 −5 −4 −3 −2 −1 1 2 3 4 5 5 10 15 20 25
- 5. Math 1000 Stuart Jones Cubic Function: y = x3 −3 −2 −1 1 2 3 −27 −18 −9 9 18 27
- 6. Math 1000 Stuart Jones Rational Function: y = 1 x −5 −4 −3 −2 −1 1 2 3 4 5 −2 −1 1 2
- 7. Math 1000 Stuart Jones Absolute Value Function: y=—x— −5 −4 −3 −2 −1 1 2 3 4 5 1 2 3 4 5
- 8. Math 1000 Stuart Jones Square Root Function: y = √ x 4 8 12 16 1 2 3 4
- 9. Math 1000 Stuart Jones Cube Root Function: y = 3 √ x −10 −5 5 10 −2 −1 1 2
- 10. Math 1000 Stuart Jones We can test to see if a function is a function using the vertical line test. You can check that all of the graphs shown previously in this section are functions. Can you draw some graphs that are not functions?
- 11. Math 1000 Stuart Jones To Be Continued...Really! The rest of these slides will be done AFTER we complete 2.6, which we will be doing next. (Yes, we’re skipping ahead.) Then, we will come back and graph piecewise functions.
- 12. Math 1000 Stuart Jones Steps for graphing a Piecewise Function: 1 Graph the first piece. 2 Erase where the first piece doesn’t apply. 3 Graph the second piece. Etc. 4 Place your open holes/closed dots.
- 13. Math 1000 Stuart Jones Graph the following: f (x) = 2x + 1 x ≤ −1 −x − 4 x > −1
- 14. Math 1000 Stuart Jones Graph the following: f (x) = −x − 1 x ≤ 0 x2 + 1 0 < x ≤ 2 4 x > 2
- 15. Math 1000 Stuart Jones Graph the following: f (x) = −x3 x < 0 √ x x ≥ 0
- 16. Math 1000 Stuart Jones The Bottom Line You can use a T-table to primitively graph functions. This is somewhat inaccurate and slow, though. Piecewise functions can be plotted by plotting each graph separately, erasing areas where its rules don’t apply, then plotting the open/closed points. Open/closed circles will always come in pairs. But sometimes, the piecewise function will join together and not have jumps.