A few Algebra 2 Questions, please help.?

Question

1. Suppose that y varies inversely with x. Write a function that models the inverse function. 

x = 7 when y = 3 

A. y=21/x 

B. y=21x 

C. y=3/7x 

D. y=3x/7 


2. Graph the rational function y=x^2-3/x-1. Both branches of the rational function pass through which quadrant? 


A. Quadrant 1 

B. Quadrant 4 

C.Quadrant 2 

D. Quadrant 3 


3. z varies inversely with x and directly with y. When x = 6 and y = 2, z = 5. 

What is the value of z when x = 4 and y = 9? 

A. 72/5 

B. 135 

C. 45 

D. 20/9

 

 

Answer 1

(1).

The word y varies inversely with x represents the function , where k is constant.

To find the value of k substitute in the above function.

The function is

The option A is correct.

Answer 2

(3).

The word z varies inversely with x and directly with y represents the function , where k is constant.

To find the value of k, substitute in the above function.

The function is

To find the value of z, substitute in the above function.

None of these options are correct.

Answer 3

The rational function is y = (x² - 3)/(x - 1) and its graph is

Observe the graph, both branches of the rational function pass through the first quadrant.

The option A is correct.