For each value of kk specified in parts (a)–(e), plot the set of points in the plane that satisfy the equation
x2 − y2 = k.
a. k = 4
b. k = 1
c. k = 1 / 4
d. k = 0
e. k = − 1 / 4
f. k = −1
g. k = −4
h. describe the hyperbolas x2 − y2 = k for different values of k. consider both positive and negative values of
kk, and consider values of k close to zero and far from zero.
i. are there any values of k so that the equation x2 − y2 = k has no solution?

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

-4, -2, 1, 4

step-by-step explanation:

domain = x values

range = y values