## Related questions with answers

Question

Find the domain, vertical asymptote, and x-intercept of the logarithmic function, and sketch its graph by hand. $y=2+\log _{10}(x+1)$

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 2$y=2+log_{10}(x+1)$

Domain: $<-1,\infty>$ There are vertical asymptote at $y=-1$.

x-intercept:

$\begin{align*} 2+log_{10}(x+1)&=0\\ log_{10}(x+1)&=-2\\ x+1&=10^{-2}\\ x&=-\frac{99}{100} \end{align*}$

The x-intercept is $\left(-\frac{99}{100},0\right)$.

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