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Graphs of Functions

Graphs of Functions. Mr. Sharpless’s 11 th Grade Mathematics Class. Click to continue. Linear. Polynomial. Absolute Value. Quadratic. Square root. Rational. Greatest Integer. Sinusoids. Click for quiz. Linear. Graphs a line The general form is: F(x)= mx+b

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Graphs of Functions

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  1. Graphs of Functions Mr. Sharpless’s 11th Grade Mathematics Class Click to continue

  2. Linear Polynomial Absolute Value Quadratic Square root Rational Greatest Integer Sinusoids Click for quiz

  3. Linear • Graphs a line • The general form is: F(x)=mx+b • M is the slope of the line • B is where the line crosses the y-axis • Practical Use: Distance travel at a constant speed Back to main menu

  4. Quadratic • Graphs a Parabola. • Standard form: F(x)=Ax2+Bx+C • Vertex Form: F(x)=a(x-h)2+k • A is the Stretch of the graph • -H is the horizontal shift • K is the Vertical shift • Practical Use: A ball throw straight up is the air. Back to main menu

  5. Absolute Value • Graphs a “V” • The general Form: F(x)=a|x-h|+k • a is the stretch of the graph • -h is horizontal shift • k is the vertical shift • Practical use: Distance as one passes the reference point Back to main menu

  6. Polynomials • Graphs “hills and valleys” • Standard form: F(x)=xn+xn-1+xn-2 … +x2+x+c • Use Critical Points to graph this function. • Practical Use: Falcon’s height over time. Back to main menu

  7. Square root • Graphs half of a sideways parabola . • F(x) = a√(b(x-h))+k • A is the stretch of the graph • H is the horizontal shift • K is the vertical shift • Practical Use: Distance vs time with a decelerating car. Back to main menu

  8. Rational graph • Graphs disconjoined curves. • F(x)= • f(x) and g(x) are both polynomial functions Back to main menu

  9. Sinusoids • Graph a oscillating curve. • F(x) = a sin(bx – c) + d or F(x) = a cos(bx– c) + d • A is the amplitude. • B is the period • C is the horizontal shift • D is the vertical shift • Practical Uses: AC Electrical Current vs time. Back to main menu

  10. Greater Integer • Graphs “steps” • F(x) = • A affects the step’s spacing • B affects the step’s length • C shifts the graph vertically. • Practical Use: Price of mailing a package vs weigh of package. Back to main menu

  11. Quiz Click on the correct answer: Which function would graph an oscillating curve? • F(x) = (X2 +1)/x • F(x) = Sin (2x) • F(x) = X + 4 • F(x) = |x - 3| + 4

  12. Sorry, F(x) = (X2 +1)/x graphs disconjoinedcurves Click here to try again

  13. That’s Correct Click to finish

  14. Sorry, F(x) = X + 4 graphs a line. Click here to try again

  15. Sorry, F(x) = |x - 3| + 4 graphs a “V” Click here to try again

  16. You have completed the graph of functions lesson. Congratulations! Click on the trophy to return to the first slide for the next student.

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