How do I find the domain and y-intercept

Question

y=log base4(2x+1)-3 ?

Answer 1

y - intercept is x = 0

Given the equation is y = log₄(2x + 1) - 3

substitute x = 0 in the equation.

y = log₄(2(0) + 1) - 3

y = log₄(0+ 1) - 3

y = log₄(1) - 3

We know that log₄(1) = 0

y = 0 - 3

y = - 3

That's your y intercept is -3

Domain [x, y] = [0, -3]

 

I hope this can be useful

Comments

Also find the domain of the function ........

Answer 2

Note :

The argument of a log of any base must be positive.

• The function is y = log₄(2x + 1) - 3.

In this case, we must use

2x + 1 >0

2x > - 1

x > - 1/2.

The domain of the function is {x Є R : x > - 1/2}, where R is the set of all real values.

• To find the y - intercept, substitute x = 0 in y = log₄(2x + 1) - 3.

y = log₄(2(0) + 1) - 3

y = log₄(0 + 1) - 3

y = log₄(1) - 3

y = 0 - 3                           (∴ log₄(1) = 0 )

y = - 3.

The y - intercept of the function is - 3.