Graphs of Functions
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Transcript of Graphs of Functions
Graphs of Functions
Mr. Sharpless’s11th Grade
Mathematics Class
Click to continue
Linear
Quadratic
Polynomial
Rational
Greatest Integer
Absolute Value
Sinusoids
Square root
Click for quiz
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
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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.
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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
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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.
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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.
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Rational graph
• Graphs disconjoined curves.
• F(x)= • f(x) and g(x)
are both polynomial functions
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Sinusoids
• Graph a oscillating curve.
• F(x) = a sin(bx – c) + dor 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.
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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.
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Quiz
Click on the correct answer: Which function would graph an oscillating curve?
A) F(x) = (X2 +1)/xB) F(x) = Sin (2x)C) F(x) = X + 4D)F(x) = |x - 3| + 4
Sorry, F(x) = (X2 +1)/x graphs disconjoined curves
Click here to try again
That’s Correct
Click to finish
Sorry, F(x) = X + 4 graphs a line.
Click here to try again
Sorry, F(x) = |x - 3| + 4 graphs a “V”
Click here to try again
You have completed the graph of functions lesson.
Congratulations!
Click on the trophy to return to the first slide for the next student.