Question

Which logarithmic function has a y-intercept?

Answer 1

Hello : 
answer A. f(x) = log(x + 1) – 1  because f(o) exist : f(o) = log(0+1)-1 = log(1)-1 =-1   ...log1=0
a y-intercept is : -1

Answer 2

Answer:

f(x) = log(x + 1) – 1 ha a y-intercept.

Step-by-step explanation:

Y-intercept is a point where the graph intersects the y-axis. And at y-axis the x-coordinate is zero.

Hence, for y-intercept, x=0

All the given functions are logarithm and we will substitute x =0, to find the y-intercept.

Logarithm function is defined only when x>0.

All the functions except the first one are undefined for x =0. Let us see how.

For B, plug x=0

f(x) = log0 + 1

Since, log 0 is undefined, hence there is no y-intercept.

For C, plug x=0

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

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

Since, log -1 is undefined, hence there is no y-intercept.

For D, plug x=0

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

f(x)=log (-1) -1

Since, log -1 is undefined, hence there is no y-intercept.

Hence all these have no y-intercept.

Now check for A

Set x=0

f(0) = log(0 + 1) – 1

=log1 -1

=0-1

=-1

Hence, the function has a y-intercept of -1.

Thus, f(x) = log(x + 1) – 1 ha a y-intercept.