Question

Use the function below to answer the following questions. y = log2 (x+4)+1 (a) Use transformations of the graph of y = log2 x to graph the given function. (b) Write the domain and range in interval notation. (c) Write an equation of the asymptote.

Answer 1

Solution:

(a)

$y=\log_3x$

f (x + 4) shifts the function 4 units to the left.

$y=\log_3(x+4)$

f (x) + 1 shifts the function 1 units upward.

$y=\log_3(x+4)+1$

(b)

$\mathrm{Domain\:of\:}\:y=\log _3\left(x+4\right)+1\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x>-4\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-4,\:\infty \:\right)\end{bmatrix}$

$\mathrm{Range\:of\:}y=\log _3\left(x+4\right)+1:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<f\left(x\right)<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}$

(c)

An asymptote is a line that a curve approaches, but never touches.

$\mathrm{Vertical\:asymptotes\:of\:}y=\log _3\left(x+4\right)+1:\quad x=-4$