Vertical & Horizontal Asymptotes
What is a vertical asymptote?
A line (x = a) where the function approaches infinity or negative infinity as (x) approaches (a).
What is a zero of a function?
The x-value where y equals zero (where it crosses the x-axis/ x intercept)
What is the inverse of the exponential function (f(x) = 2^x)?
(f^{-1}(x) = \log_2(x))
What is the slope of the line (y = 5x - 3)?
m = 5
What is the common difference in the sequence 3, 7, 11, 15, ...?
4
What is a horizontal asymptote?
A line (y = b) that the graph of a function approaches as (x) goes to infinity or negative infinity.
Solve for the zero: (f(x) = 2x - 6).
(x = 3)
Simplify: (\log_{10}(1000)).
3
Find the equation of the line passing through (0,2) with slope -4.
(y = -4x + 2)
Find the 10th term of the arithmetic sequence: 2, 6, 10, ...
38
Find the vertical asymptote of (f(x) = \frac{1}{x-3}).
(x = 3)
Describe what a hole in a function’s graph represents.
A point where the function is undefined due to a common factor in the numerator and denominator (removable discontinuity)
What is the domain of (f(x) = \log(x-2))?
(x > 2)
What is the y-intercept of (y = -2x + 7)?
7
What is the common ratio of the sequence 2, 6, 18, 54, ...?
3
Find the horizontal asymptote of (f(x) = \frac{2x}{x+1}).
(y = 2)
For (f(x) = \frac{x^2 - 9}{x - 3}), where is the hole?
At (x = 3)
Solve for (x): (\log_3(x) = 4).
(x = 81)
Write the equation of a line in point-slope form given point (2, -1) and slope 3.
(y + 1 = 3(x - 2))
Find the sum of the first 5 terms of the geometric sequence: 1, 2, 4, 8, ...
31
Find all vertical and horizontal asymptotes of (f(x) = \frac{x^2 - 1}{x^2 - 4}).
Vertical: (x = 2, x = -2); Horizontal: (y = 1)
Find all zeros of (f(x) = x^2 - 4).
(x = 2) and (x = -2)
(\log_2(8) + \log_2(x) = 3 + \log_2(x))
simplify
(\log_2(8x))
If two lines are perpendicular, what is true about their slopes?
Their slopes are negative reciprocals
What is the formula for the nth term of an arithmetic sequence with first term (a_1) and common difference (d)?
(a_n = a_1 + (n-1)d)