Key Features of Rational Functions (day 2)

Key Features of Rational Functions (day 2)

Domain, Range, End Behavior

Evaluating Rational Functions Algebraically

• Ex: evaluate  $f\left(x\right)=\frac{x}{x+3}\ at\ f\left(2\right)$  

• Two methods: either plug in 2 in place of all the x's, or look at the graph and see where graph is at x=2!

Multiple Choice

Given:   $f\left(x\right)=\frac{3}{x+2}+1$  

Evaluate:  $f\left(4\right)$  

• 1.75

• 1.5

• 2

• 0.67

Fill in the Blank

Use the graph to evaluate $f\left(2\right)$  .

End Behavior of Rational Functions

•  The same as evaluating rational functions, this time just do it at    $\pm\infty$  (because this is what we look at for end behavior) !!

• Easy method: plug in 1,000; 10,000; and 100,000 for x to see where our f(x) is approaching. This will be our end behavior.

Multiple Choice

Remember, y is the same thing as f(x).

• The end behavior of the graph is x →∞, y→∞ and x→∞, y→⁻∞

• The end behavior of the graph is x →∞, y→∞ and x→⁻∞, y→∞

• The end behavior of the graph is x →∞, y→∞ and x→⁻∞, y→0

• The end behavior of the graph is x →∞,y→0 and x→∞, y→⁻∞

Multiple Choice

Describe the end behavior of the graph.

• x →∞, y→⁻∞ and x →⁻∞,y→⁻∞
• x →∞, y→∞ and x→⁻∞, y→∞
• x →∞, y→∞ and x→⁻∞, y→2
• x →∞,y→2 and x→⁻∞, y→∞

Multiple Choice

What is the end behavior as x approaches negative infinity?

• y approaches negative infinity

• y approaches positive infinity

• y approaches 1

• y approaches 2