Reference no: EM13675378

Describe the effect of changes to the constant b in f(x) = |x| ± b.

C. Graph and label the following three functions:

• f(x) = -2x + 3
• g(x) = -2x - 3
• h(x) = (1/2)x

1. Describe the domain and range for each of these functions.

2. Explain the geometric relationship between the graphs of f(x) and g(x).

3. Explain the geometric relationship between the graphs of g(x) and h(x).

E. Graph and label the following two functions making sure that missing points and asymptotes are clearly identified:

• f(x) = (x2 + 7x + 12)/(x + 4)
• g(x) = (- x2 + 3x + 9)/(x - 1)

1. Describe the domain and range for each of these functions.

2. Determine the equation(s) of any asymptotes found in the graphs of these functions, showing all work.

3. Discuss the conditions needed for a rational function to contain a slant asymptote and any special cases that affect slant asymptotes.

G. Graph and label the following two functions:

• f(x) = 3^x
• g(x) = (1/3)^x

1. Describe the domain and range for each of these functions.

2. Describe the important features of these graphs.

H. Graph and label the following three functions:

• f(x) = √x
• g(x) = ⁴√x
• h(x) = ⁵√x

1. Describe the domain and range for each of these functions.

2. Explain what common properties these graphs share (e.g., common points, shape, domain, range).

3. Explain why the graphs of g(x) and h(x) are different.

1. Graph and label the following two functions:

• f(x) = log₁₂x
• g(x) = log₂x

1. Describe the domain and range for each of these functions.

2. Find the inverse function of f(x), showing all work.