Question

Consider the function ?(?) = log3(3? + 15) − 4. Use algebra to determine the domain, range, asymptote, ?-intercept, and ?-intercept (if any). [6 pts] Sketch the graph. [4

Answer 1

f(x) = log 3 ( 3x + 15 ) - 4

domain

3x + 15 > 0

3x > -15

x > -5

domain is ( -5 , infinity )

range is ( - infinity , + infinity )

asymptote is

x = - 5

x intercept

log3(3? + 15) − 4 = 0

adding 4 on both sides

log 3 ( 3x + 15 ) = 4

chnging to exponential form

3x+15 = 3^4

3x + 15 = 81

subtrcat 15 from both sides

3x = 66

x = 22

x intercept is ( 22, 0 )

to find y intercept plug x = 0

log3(3(0) + 15) − 4 = y

log 3 (15) - 4 = y

y = - 1.535

y intecept is ( 0 , -1.535)