Attributes and Transformations of the Natural Logarithm Func

Name the function:

 $y=e^x$  

• logarithmic parent function

• natural logarithm function

• natural base exponential function

Name the function:

 $y=\ln\ x$  

• logarithmic parent function

• natural logarithm function

• natural base exponential function

Name the function:

 $y=\log\ x$  

• logarithmic parent function

• natural logarithm function

• natural base exponential function

Analyze the domain, range, x-intercept, and asymptote of the graph of:

 $y=\log_ex+1$  

• Domain: All real numbers, Range: y > 0, x-intercept: (0.368, 0), Asymptote: y = 0

• Domain: x > 0, Range: All Real numbers, x-intercept: (0.368, 0), Asymptote: y = 0

• Domain: x > 0, Range: All Real numbers, x-intercept: (0.368, 0), Asymptote: x = 0

• Domain: x > 0, Range: All Real numbers, x-intercept: (0, 0.368), Asymptote: y = 0

Logarithms are ___________ for negatives and zero.

Sketch the graph of the pair of functions on the same coordinate grid (or desmos). Identify the transformation that maps the first function to the second function. Determine the effect the transformation has on the intercepts.

 $f\left(x\right)=\log_ex,\ g\left(x\right)=\log_e\left(x-4\right)$  

• The graph shifts up 4 units.

• The graph shifts down 4 units.

• The graph shifts right 4 units.

• The graph shifts left 4 units.

Let f(x) = ln x. Identify the minimum and maximum values over the specified interval, or state that a maximum or minimum does not exist. [1, 5]

Write the equation of the transformation of the parent function y = loge x that is reflected across the x-axis, shifted 3 units up, and then shifted 1 unit right.

• - ln (x - 1) - 3

• - ln (x + 1) + 3

• ln (-x - 1) + 3

• - ln (x - 1) + 3

What is the asymptote and the x-intercept?
 $f\left(x\right)=\ln x+2$  

• x = 0

• x = -2

• (0.135, 0)

• (0, 0.135)
  

What is the asymptote and the x-intercept?
 $f\left(x\right)=\ln\left(x+2\right)$  

• x = 2

• x = -2

• (-1, 0)

• (0, 1)