Functions and Sequences Assessment

The video tutorial covers various mathematical concepts, including sequences, arithmetic sequences, inverse functions, domain restrictions, graphing, asymptotes, and logarithms. The instructor explains how to write explicit rules for sequences, discusses common differences in arithmetic sequences, and explores inverse functions with domain restrictions. The tutorial also covers graphing techniques, understanding asymptotes, and concludes with a discussion on logarithms.

What is the first term of the given sequence?

• 25

• 125

• 5

• 1

How do you determine the common difference in an arithmetic sequence?

• By subtracting consecutive terms

• By dividing the terms

• By multiplying the terms

• By adding consecutive terms

What is the formula to find the nth term in an arithmetic sequence?

• a_n = a_1 + (n-1)d

• a_n = a_1 * r^(n-1)

• a_n = a_1 / (n-1)

• a_n = a_1 - (n-1)d

What is the inverse of a function?

• A function that reflects over the y-axis

• A function that divides the original function

• A function that multiplies the original function

• A function that reflects over the line y=x

How do you find the inverse of a function?

• Add 1 to the function

• Switch x and y and solve for y

• Multiply the function by -1

• Divide the function by 2

What is the domain of the inverse function if the original function's range is not zero?

• The domain is the same as the original function's domain

• The domain is not zero

• The domain is the same as the original function's range

• The domain is zero

What is the horizontal asymptote of the function y = 2^x + 3?

• y = 2

• x = 3

• y = 3

• x = 2

What is the y-intercept of the function y = 2^x + 3?

• (0, 3)

• (0, 2)

• (0, 4)

• (0, 5)

What is the equation of the vertical asymptote for the logarithmic function log_2(x-4) + 2?

• x = 2

• x = 4

• y = 2

• y = 4

What is the average rate of change of the function y = 2^x + 3 from x = 2 to x = 5?

• 4/3

• 11/3

• 5/3

• 7/3