Key Features of Graphs of Rational Expressions

Presentation

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Mathematics

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10th - 12th Grade

•

Medium

•

CCSS

HSF-IF.C.7D, HSA-REI.B.4B, HSF-IF.C.7A

Standards-aligned

Jordan Owens

Used 16+ times

FREE Resource

9 Slides • 7 Questions

Key Features of Graphs of Rational Expressions

Advanced Algebra

Multiple Choice

$f\left(x\right)=x^2-5x-6$

Bell Ringer: Factor and Solve the Equation

$x=-5,\ x=-6$

$x=5,\ x=6$

$x=-1,\ x=6$

$x=1,\ x=-6$

Open Ended

You have 60 seconds! Find a partner that is sitting around you. When you have found your partner, submit both of your names as the answer to this question.

Type response here

REVIEW

f\left(x\right)=x^3+x^2-4x-4

x-int:
y-int:
Asymptotes:
Domain:
Range:
End Behavior:

$As\ x\ \longrightarrow\ -\infty,\ f\left(x\right)\ \longrightarrow\$ $As\ x\ \longrightarrow\ \infty,\ f\left(x\right)\ \longrightarrow\$

Multiple Choice

What was the x-int of the previous problem?

$\left(-2,0\right),\ \left(-1,0\right),\ \left(2,0\right)$

$\left(0,-2\right),\ \left(0,-1\right),\ \left(0,2\right)$

$\left(-4,0\right)$

$\left(0,-4\right)$

REVIEW

$f\left(x\right)=2^x-4$

x-int:
y-int:
Asymptotes:
Domain:
Range:
End Behavior:

As\ x\ \longrightarrow\ -\infty,\ f\left(x\right)\ \longrightarrow\

As\ x\ \longrightarrow\ \infty,\ f\left(x\right)\ \longrightarrow\

Multiple Choice

What was the horizontal asymptote of the previous question?

$y=-3$

$y=-4$

$x=-3$

$x=-4$

What about this one?

f\left(x\right)=\frac{1}{x^2}

x-int:
y-int:
Asymptotes:
Domain:
Range:
End Behavior:

As\ x\ \longrightarrow\ -\infty,\ f\left(x\right)\ \longrightarrow\

As\ x\ \longrightarrow\ \infty,\ f\left(x\right)\ \longrightarrow\

Open Ended

What was different about the graph we just saw compared with the two previous graphs?

Type response here

Welcome to Rational Expressions!

Definition: Rational Expressions are Fractional Expressions where the Degree of the Denominator is Greater than 0
What does that mean?

Let's talk about the Asymptotes

Horizontal Asymptotes (ALWAYS y= )
Vertical Asymptotes (ALWAYS x= )
But there are also...

Slant Asymptotes

Found by Using Long Division
Written as the equation of a line (y=mx+b)
Don't worry! We will learn more about these tomorrow!

Let's try an example (without partners)

$f\left(x\right)=\frac{x}{x+1}$

x-int:
y-int:
Asymptotes:
Domain:
Range:
End Behavior:

As\ x\ \longrightarrow\ -\infty,\ f\left(x\right)\ \longrightarrow\

As\ x\ \longrightarrow\ \infty,\ f\left(x\right)\ \longrightarrow\

Multiple Choice

What is the Domain and Range of the previous graph?

D:\ \left(-\infty,\ \infty\right)

R:\ \left(-\infty,\ \infty\right)

$D:\ \left(-\infty,\ -1\right)\cup\left(-1,\ \infty\right)$ $R:\ \left(-\infty,\ 1\right)\cup\left(1,\ \infty\right)$

$D:\ \left(-\infty,\ 1\right)\cup\left(1,\ \infty\right)$ $R:\ \left(-\infty,\ -1\right)\cup\left(-1,\ \infty\right)$

Poll

Which key features are still confusing you?

Intercepts

Domain/Range

Asymptotes

End Behavior

TOTD (Individually)

$f\left(x\right)=\frac{2x}{x-3}$

x-int:

y-int:

Asymptotes:

Domain:

Range:

End Behavior: $As\ x\ \longrightarrow\ -\infty,\ f\left(x\right)\ \longrightarrow\$ $As\ x\ \longrightarrow\ \infty,\ f\left(x\right)\ \longrightarrow\$

Key Features of Graphs of Rational Expressions

Advanced Algebra

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