Match each pair of functions to the phrase that best describes the difference between f(x) and g(x). 100 points

See the attachment

A vertical shift adds a constant to the function value. f(x) ⇒ f(x)+5 is a vertical shift up 5 units.

A horizontal shift subtracts a constant from the independent variable value. f(x) ⇒ f(x-5) is a shift right 5 units.

A multiplying factor of magnitude greater than 1 is a vertical expansion; less than 1 represents a vertical compression. f(x) ⇒ -5f(x) is a vertical expansion (and reflection over the x-axis). f(x) ⇒ (1/2)f(x) is a vertical compression.

_____

Comment on the vertical compression

You have the function f(x) = x² +2 being transformed to g(x) = (1/2)x² +2. If this were a straight vertical compression, the function g(x) would look like ...

... g(x) = (1/2)(x² +2) = (1/2)x² +1

The fact that the constant has remained +2, instead of being enclosed in parentheses or changing to +1, means that the graph has been compressed vertically around the point (0, 2), not the origin.

a rotation about point l

step-by-step explanation:

quizlet

e^-kt = n/n0 = 0.79  

-kt = ln 0.79  

t = - ln 0.79/0.0001  

= 2357 years

step-by-step explanation: