Functions: Domain, Range and Composition
Functions: Inverses
Functions: Transformations
Exponents
Logarithms
100
You're in a firing squad. The squad knows that there is a term for the WIDTH of how far they can shoot as well as a different term for the LENGTH, or DISTANCE. One of the men thinks the terms domain and range would work, but can't remember which is which! Which is domain, width or length? Which is range?
What is: Domain would be width (horisontal, on the x-axis.) Range would be length (vertical, on the y-axis)
100
What are two ways you can plot an inverse on the same axis as it's function?
What is: a) make a table of points, then switch the x and y values and re-plot. b) draw a line of symmetry through the origin (as in an odd function) and the make the function symmetrical across it.
100
What does [f(x) = (x+3)^2] look like in comparison to [f(x) = x^2]
What is: The same function translates three points to the left.
100
What is an example of exponential growth in our world?
What is bacteria, interest, etc.
100
The inverse of an exponential equation
What is a logarithm?
200
How would you write that a function had a domain restricted from -3 to 3 in interval notation and otherwise?
What is: (-3, 3) or −3 ≤ x ≤ 3
200
What is the inverse of x^3?
What is: cube-root of x.
200
If my function if [f(x) = x^2], what transformations would give it: Domain: (-infinity, infinity) Range: (-infinity, -3)
What is: [f(x) = -x^2 - 3] (Make x negative, minus three)
200
Rewrite these as powers of ten: 1) 10000 2) 0.0001
What is: 1) 10^4 2) 10^-4
200
log(a) + log(b) =
What is log(ab) ?
300
Give the domain and rane of the parent function y = √(1 − x^2)
What is: Domain: (-1, 1) Range: (0, 1)
300
In order for a function to have an inverse, it must be what?
What is one-to-one?
300
In my function [f(x) = x] will [f(x)= 1/3x^2] cause a stretch or a squeeze?
What is a stretch?
300
a^x * b^x = ?
What is: ab^x
300
Rewrite [log(b,y) = x] in a manner other than [y = b^x]
What is [x = log(y) / log(b) ]
400
List the domain and range of the cubic function, the quadratic function and the square-root function.
What is: cubic: d: ℝ r: ℝ quadratic: d: ℝ r: [0, infinity) square-root: d: [0, infinity) r: [0, infinity)
400
What is the inverse of f(x)=2x+1?
What is f(x)=(x-1)/2
400
Compared to the parent, what does [f(x) = -x^3] look like?
What is the same function, just flipped over the y-axis.
400
If 10^0.301 = 2 and 10^0.477 = 3, solve for x in the below equation: 10^x = 3/2
What is: 10^x = 10^0.477/10^0.301 0.477-0.301 = 0.176 10^x = 10^0.176 x = 0.176
400
If [3.2^x = 1], without calculating, what is x?
What is zero (0)?
500
What is the domain and range of the parent rational function?
What is: Domain: (−infinity, 0) AND (0, infinity) Range: (−infinity, 0) AND (0, infinity)
500
If my function is f(x) = rubber duck, than what is the inverse of my function?
What is ƒ−1(x).
500
Describe the transformations done to the parent function to create this instead: [f(x) = 2^(1/3(x-2)) + 3]
What is: moved up 3, 2 to the left and a stretch of 3.
500
Prove that [a^-1 = 1/a] using the fact that [a^m/a^n = a^m-n]
What is: [a^0 = 1] and [a^1 = a] 1/a = a^0/a^1 a^0/a^1 = a^0-1 a^0-1 = a^-1
500
Is [log(b)^x = log(y)] equivalent to [x*log(b) = log(y)]
What is yes, yes it is.