Examine the function `f(x) = (x^2+5)/(3x+1)` in the domain (1,7) and state its type of discontinuity

Hello from MrBillDoesMath!

The function is continuous on (1,7)

Discussion:

See attached graph. The discontinuity in the function occurs when

3x + 1 =0   =>

x = - (1/3)

but that x value does not lie in the interval  (1.7). So there is no discontinuity on (1,7).    

FYI:  the discontinuity at -1/3 is a non-removable discontinuity

Thank you,

MrB

$450.00 for 6 weeks

or

$300

step-by-step explanation:

$200.00 for first week $50.00 x5 equals $250 plus $200 equals $450.00 for six weeks.

$200 for first week

$200 x 0.10 = $20

$20 x 5 = $100

$200 + $100 = $300

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)