Rational Equation by Graphing

Graphing Rational Functions

March 2, 2021

Multiple Choice

What are the equations of the  vertical asymptotes for f(x)?

$$f\left(x\right)=\frac{\left(x-1\right)\left(x+3\right)}{\left(x+3\right)\left(x+4\right)}$$  

• $$x=-3$$  

• $$x=-3\ and\ x\ =\ -4$$  

• $$x=-4$$  

• $$x=1$$  

• None

Multiple Choice

At which x-value(s) does the graph of

$$f\left(x\right)=\frac{\left(x-1\right)\left(x+3\right)}{\left(x+3\right)\left(x+4\right)}$$  have a hole?

• $$x=1$$  

• $$x\ =\ -3$$  

• $$x=\ -4$$  

• No holes

Multiple Choice

The answer to the last problem is a hole occurs at x = -3. What is the y-coordinate of the hole?

$$f\left(x\right)=\frac{\left(x-1\right)\left(x+3\right)}{\left(x+3\right)\left(x+4\right)}$$  

• 1

• -4

• -3

• Can't be determined

Multiple Choice

Where does

$$f\left(x\right)=\frac{\left(x-1\right)\left(x+3\right)}{\left(x+3\right)\left(x+4\right)}$$  have any horizontal asymptotes?

• $$y\ =\ -4$$  

• $$y=\ 1$$  

• $$y=\ -3$$  

• $$y=1$$  

• No horizontal asymptote

Multiple Choice

Where does

$$f\left(x\right)=\frac{\left(x-1\right)\left(x+3\right)}{\left(x+3\right)\left(x+4\right)}$$  have a y-intercept?

• $$\left(0,\ -\frac{1}{4}\right)$$  

• $$\left(0,0\right)$$  

• $$\left(0,-3\right)$$  

• $$\left(0,\frac{3}{4}\right)$$  

• No y-intercept

Multiple Choice

Where does

$$f\left(x\right)=\frac{\left(x-1\right)\left(x+3\right)}{\left(x+3\right)\left(x+4\right)}$$  have an x-intercept?

• $$\left(1,0\right)\ and\ \left(-3,0\right)$$  

• $$\left(-3,0\right)$$  

• $$\left(1,0\right)$$  

• $$\left(-4,0\right)$$  

• No x-intercepts

Open Ended

Wrrite the equation

CHALLENGE!!

See if you can write a possible equation for this graph:

Open Ended

Equation:

Let's look at the HW

Open Ended