Show:
Functions: Domain, Range, Composition
Functions: Inverses
Functions: Transformations
Exponents
Logarithms
100
What is the definition of a function?
What is a relation between two sets of numbers. For every input there is only one output.
100
What line is the visual indicator of whether two functions are inverse?
What is y=x
100
How do you flip y=√x over the y-axis?
What is y=√-x
100
What is 5^10 x 5^2
What is 5^12
100
What is log(1000)?
What is 3
200
In interval notation, write the domain and range of y=x^2
What is domain=[0, ∞) and range=[0, ∞)
200
What is a one-to-one function? What two “tests” does it pass?
What is in a function, for every input there is only one output. If a function is one-to-one, then the opposite is true as well. For every output, there is only one input. This would mean that the graph of the function would pass both a vertical line test and a horizontal line test.
200
How do you flip y=2^x over the x-axis, move it to the right 5 and up 2?
What is y=-2^(x-5)+2
200
What is 3^12 x 243^3
What is 3^20
200
What is log5(25)+log10(100)?
What is 4
300
In interval notation, write the domain and range for a function with... a) a domain less than or equal to 10 and greater than one AND a range greater than -5. b) both a domain and range of all real numbers.
What is a) domain=(-1, 10], range=(-5, ∞) b) domain=(-∞, ∞), range= (-∞, ∞)
300
What is the equation for the inverse of the function f(x)=3x-5?
What is (x+5)/3=f(x)^-1
300
Originally f(x)... If a>1, f(a*x) ______ the graph horizontally and a*f(x) _______ the graph vertically.
What is "shrinks," what is "stretches"
300
Simplify (3^-2/4^6)^5 with no negative exponents.
What is 4^30/3^10
300
Why does log(.5)=the negative of log(2)?
What is .5=1/2 (a negative flips 2 so it becomes 1/2) so log(1/2)=-x--> 10^-x=(1/2)
400
Which function (with no transformations) has a y-intercept of 1 and an asymptote of x=0
What is y=2^x (exponential function)
400
Find the intersection of f(x)=2x-1 and its inverse.
What is (1,1)
400
How do you transform y=|x| so that it is horizontally stretched by a factor of 3 and vertically shrunk by a factor of 2?
What is y=(1/2)|(1/3)x|
400
Justify why b^m/b^n=b^m-n
What is b^m/b^n=b^m*(1/b^n) (1/b^n)=b^-n so b^m*b^-n=b^m-n
400
Explain why it is predictable that log(64)=3*log(4).
What is log(64)-->10^x=64 log(4)-->10^y=4-->10^3y=64 so 10^x=10^3y so x=3y so log(64)=3*log(4)
500
What are the eight most important parent functions an dtheir equations?
What is - linear function, y=x - quadratic function, y=x^2 - cubic function, y=x^3 - square root function, y=√x - inverse function, y=x/2 - half circle function, y=√(1-x^2) - absolute value function, y=|x| - exponential function, y=2^x
500
f(x)= (3x+7)/(x-2). Find f^-1(x), the inverse of f(x).
What is f^-1(x)=7+2x/x-3
500
f(x)=√x and g(x)=(x+1)/2 How do you vertically stretch the graph of f(g(x)) by a factor of 2 and horizontally shrink it by a factor of 3.
What is f(g(x))=√2((1/3)x+1)/2
500
A certain element has a half-life of 2000 years. It is known that an object had 30 units of this element 30,000 years ago. About how many units does this element has now.
What is about 0.00092 units left
500
Solve for k in 2=e^6.5k
What is loge(2)/6.5=k