Lesson 19 End Behavior of Rational Functions

Lesson 19 End Behavior of Rational Functions

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Multiple Choice

What is the end behavior of y=f(x)?

 $f\left(x\right)=\frac{5x+2}{x-3}=5+\frac{17}{x-3}$  

• As x increases, y approaches 5.  As x decreases y approaches -5.

• As x increases, y approaches -5.  As x decreases y approaches -5.

• As x increases, y approaches 5.  As x decreases y approaches 5.

• As x increases, y approaches -5.  As x decreases y approaches5.

Multiple Choice

Rewrite the rational function in the form

 $g\left(x\right)=p\left(x\right)+\frac{r}{x+2}$  where p(x) is a polynomial and r is an integer.
 $g\left(x\right)=\frac{x^2+7x-12}{x+2}$  

•  $g\left(x\right)=x+5+\frac{22}{x+2}$  

•  $g\left(x\right)=x+5-\frac{22}{x+2}$  

•  $g\left(x\right)=x-5+\frac{22}{x+2}$  

•  $g\left(x\right)=x-5-\frac{22}{x+2}$  

Multiple Choice

 $p\left(x\right)=\frac{3}{x-1}$  

Match the polynomial with its end behavior.

• The graph approaches y=2.

• The graph approaches y=3.

• The  graph approaches y=2x+3

• The graph approaches  $y=x^2+x+1$  

• The graph approaches y=0.

Multiple Choice

 $p\left(x\right)=\frac{2x}{x-1}$  

Match the polynomial with its end behavior.

• The graph approaches y=2.

• The graph approaches y=3.

• The  graph approaches y=2x+3

• The graph approaches  $y=x^2+x+1$  

• The graph approaches y=0.

Multiple Choice

 $p\left(x\right)=\frac{2x+3}{x-1}$  

Match the polynomial with its end behavior.

• The graph approaches y=2.

• The graph approaches y=3.

• The  graph approaches y=2x+3

• The graph approaches  $y=x^2+x+1$  

• The graph approaches y=0.

Multiple Choice

 $p\left(x\right)=\frac{2x^2+x+3}{x-1}$  

Match the polynomial with its end behavior.

• The graph approaches y=2.

• The graph approaches y=3.

• The  graph approaches y=2x+3

• The graph approaches  $y=x^2+x+1$  

• The graph approaches y=0.

Multiple Choice

 $p\left(x\right)=\frac{x^3}{x-1}$  

Match the polynomial with its end behavior.

• The graph approaches y=2.

• The graph approaches y=3.

• The  graph approaches y=2x+3

• The graph approaches  $y=x^2+x+1$  

• The graph approaches y=0.

Multiple Choice

 $P\left(x\right)=x^3+2x^2-13x+10$  

Divide P(x) by x+5.  How could we tell by looking at the remainder that (x+5) must be a factor?

• The remainder is 5

• The remainder is -5

• The remainder is 0

• The remainder is 10

Multiple Choice

 $f\left(x\right)=x^4+3x^3-x^2-3x$  

For the polynomial function f(x), we have f(-3)=0,f(-2)=-6,f(-1)=0, f(0)=0,f(1)=0,f(2)=30,f(3)=144. Rewrite f(x) as a product of linear factors.

•  $f\left(x\right)=x\left(x-1\right)\left(x+1\right)\left(x-3\right)$  

•  $f\left(x\right)=x\left(x-1\right)\left(x-1\right)\left(x+3\right)$  

•  $f\left(x\right)=x\left(x+1\right)\left(x+1\right)\left(x+3\right)$  

•  $f\left(x\right)=x\left(x-1\right)\left(x+1\right)\left(x+3\right)$  

Fill in the Blanks

 $h\left(r\right)=\frac{180}{r^2}$  

There are many cones with a volume of 60 cubic inches. The height h(r) in inches of one of these cones is a function of its radius r in inches.

What is the height of one of these cones if its radius is 2 inches?

Type the number only.

Fill in the Blanks

 $h\left(r\right)=\frac{180}{r^2}$  

There are many cones with a volume of 60 cubic inches. The height h(r) in inches of one of these cones is a function of its radius r in inches.

What is the height of one of these cones if its radius is 3 inches?

Type the number only.

Fill in the Blanks

 $h\left(r\right)=\frac{180}{r^2}$  

There are many cones with a volume of 60 cubic inches. The height h(r) in inches of one of these cones is a function of its radius r in inches.

What is the height of one of these cones if its radius is 5 inches?

Type the number only.

Multiple Choice

 $9x$  

Match each rational function with a description of its end behavior as x gets larger and larger.

• The value of the expression gets closer and closer to 0.

• The value of the expression gets closer and closer to 1.

• The value of the expression gets closer and closer to 9.

• The value of the expression is 99.

• The value of the expression gets larger and larger in the positive direction

Multiple Choice

 $\frac{9}{x}$  

Match each rational function with a description of its end behavior as x gets larger and larger.

• The value of the expression gets closer and closer to 0.

• The value of the expression gets closer and closer to 1.

• The value of the expression gets closer and closer to 9.

• The value of the expression is 99.

• The value of the expression gets larger and larger in the positive direction

Multiple Choice

 $\frac{99x}{x}$  

Match each rational function with a description of its end behavior as x gets larger and larger.

• The value of the expression gets closer and closer to 0.

• The value of the expression gets closer and closer to 1.

• The value of the expression gets closer and closer to 9.

• The value of the expression is 99.

• The value of the expression gets larger and larger in the positive direction

Multiple Choice

 $\frac{99+x}{x}$  

Match each rational function with a description of its end behavior as x gets larger and larger.

• The value of the expression gets closer and closer to 0.

• The value of the expression gets closer and closer to 1.

• The value of the expression gets closer and closer to 9.

• The value of the expression is 99.

• The value of the expression gets larger and larger in the positive direction

Multiple Choice

 $\frac{99x+x}{x}$  

Match each rational function with a description of its end behavior as x gets larger and larger.

• The value of the expression gets closer and closer to 0.

• The value of the expression gets closer and closer to 1.

• The value of the expression gets closer and closer to 9.

• The value of the expression is 99.

• The value of the expression gets larger and larger in the positive direction