Multi-Module Assignment: Exponential and Log Functions

Multi-Module Assignment: Exponential and Log Functions

Due at the end of Module 7

1. Does f(x) = ex+1 overtake f(x) = x4 – 3x + 11? Where does this occur? Determine this intersection point and show your work:

· Graphically (using Desmos). Include the image of your Desmos graph.

2. Consider the graph of the function f(x) = log3 x. The domain for this function is (0, ∞) and the range is (-∞, ∞). See the top of page 457.

Using what you know about translations, state the domain and range of the following functions:

a) g(x) = log3(x + 2)

b) g(x) = log3(x – 2)

c) g(x) = log3 (2x)

d) g(x) = log3 (x/2)

e) g(x) = log3(-x)

3. Consider the function

Does this function represent exponential growth or exponential decay? Explain how you made that determination.

4. Does the graph of a logarithmic function have a horizontal asymptote? A vertical? If so, give them.

5. Consider . Provide and use the generalization statement your team created in the discussion to answer the following:

a) Which graph is on top in the interval (0, 1)?

b) Which graph is on the top in interval (1, ∞)?