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.
