Graphs of Functions

Mr. Sharpless’s11th Grade

Mathematics Class

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Linear

Quadratic

Polynomial

Rational

Greatest Integer

Absolute Value

Sinusoids

Square root

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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

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That’s Correct

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Sorry, F(x) = X + 4 graphs a line.

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Sorry, F(x) = |x - 3| + 4 graphs a “V”

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You have completed the graph of functions lesson.

Congratulations!

Click on the trophy to return to the first slide for the next student.