Question

Which logarithmic function has a y-intercept?

f(x) = log(x + 1) – 1
f(x) = log x + 1
f(x) = log(x –1) + 1
f(x) = log(x – 1) – 1

Answer 1

The first one, f(x)=log(x+1)-1 has a y-intercept

Answer 2

Option 1 is correct.

Explanation:

We have different functions

we need to tell which one of them will have y-intercept

So, to find y-intercept we will put x=0

So, in first function put x=0 we get:

`f(0)=log(0+1)-1`

`\Rightarrow f(0)=log(1)-1`

`\Rightarrow f(0)=-1`

Hence, the first function has y-intercept.

In all the last three functions:

When we put x=0 in f(x)=log x+1

We will get log(0) which is not defined

And x=0 in f(x)=log(x-1)+1

log(-1) which is also not defined.

And x=0 in f(x)=log(x-1)-1

Again not defined.