Determine the domain of the following functions. determine where the function is continuous. if it is not continuous, state why.

a) f(x)= 3x^2 -5x +7

b)

c)

Step-by-step explanation:

a) This function is a quadratic / polynomial.  Alll polynomials are defined for all real numbers.  The domain is (-∞, ∞).

b) this function's denominator is x(x-1), which is zero at x = 0 and at x = 1.  Since we cannot divide by zero, neither 0 nor 1 is part of the domain.  Expressed in positive terms, the domain is (-∞, 0) ∪ (0, 1) ∪ (1, ∞).

c) The domain of the square root function is [0, ∞).  Given that the argument of the square root function in c) is x - 2, we find the domain by writing and solving the inequality x-2 > 0.  This comes out to x > 2 or (2, ∞)

Continuity:  (a) This function is continuous for all x.

(b) This function is continuous only for (-∞, 0) ∪ (0, 1) ∪ (1, ∞).

(c) This function is continuous only for x > 2.

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.