Algebraic Functions

Question

algebraically determine the domain and the y-intercept of the function: y = log7(4x+3)+6

Answer 1

y = log₇(4x + 3) + 6;

To get domain we set 4x + 3 > 0, x > - 3/4. So, domain is interval (- 3/4, ∞).

To get y-intercept we set x = 0, y = log₇3 + 6

Answer 2

since you can get a log for 0 or a negative number the argument 4x+3 must be >0

so 4x>-3

x>-3/4so domain is x>-3/4

to find the y intercept set x equal to 0

y = log7(3) +6= 6.56