Show:
Functions: Inverses
Functions: Transformations
Functions: Domain, Range, Composition
Exponents
Logarithms
100
This is the function in which all of the x and y values have been switched. If the point 1,4 is in the original function than the point 4,1 is in the this function. This particular function can also be thought of as the original function reflected over the line x=y.
What is the definition of the inverse of an equation?
100
This shifts the entire graph up one unit.
What is the effect of adding +1 to any function? example: f(x) = x^2 + 1.
100
The domain of a function is all of the input values, and the range of the function is all of the output values.
What is the domain, and range of a function?
100
An exponent is a small number written above and to the right of a number. It represents how many times any number will be multiplied by itself. Exponents can be negative, positive, or even fractions.
What is an exponent? Give a clear definition as to what the function of an exponent is and what it represents.
100
x = log(b)y = b^x = y
What is the log form of the equation b^x = y?
200
y = x^2 switch the x and y... x = y^2 √x = y
What is the equation of the inverse function of f(x)= x^2
200
y = √x shifted to the left five units: y = √(x+5)
What is the transformation that shifts the graph of y = √x to the left five units?
200
x = all real numbers y = all real numbers
What is the domain and range of the function y= x^3 - 1?
200
(4p^2q^3)^2 = 16p^4q^6
What is an equivalent way to write (4p^2q^3)^2?
200
10^x = 9 can be rewritten as x = log(10)9 x = 0.95
What is x in the problem 10^x =9?
300
inverse function: y = 2(x-3) + 2 original: x = 2(y-3) +2 (x+3)/2 + 1 = y
What is the original function if the inverse function is y = 2(x-3) + 2?
300
The parent function y = x has been vertically stretched by a factor of three, horizontally stretched by a factor of four, shifted right one unit, and shifted down two units.
What are all of the transformations preformed on the parent function y = x to get the function y = 3(x-1)/4 -2?
300
The domain of the function y = (√x+2)-1 = [-2, ∞) The range of the function y = (√x+2)-1 = [-1, ∞)
What is the domain and range written in interval notation of the function y = (√x+2)-1
300
5(4^x) = 25 (4^x) = 5 x = 1.17
What is What is x in the problem 5(4^x)=25? Calculators can be used.
300
log(10).25 and log (10)4 differ by a sign. This is because logarithms are exponents. These two exponents differ by a sign because .25 = 4^-1 and 4 = 4^1.
What is the similarity between log(10).25 and log(10)4?
400
For an equation to have an inverse it must be one to one. For an equation to be one to one it must past the horizontal line test, or have one input for every output.
What is the qualification an equation must meet if it has an inverse?
400
(0,0) is the point on the graph y = x^2 not affected by a vertical stretch of three.
What is the point on the graph y = x^2 that is not affected by vertically stretching the function by a factor of three?
400
In the function y = (x^3)/2 the domain is expanded by a factor of two. In the function y = (x^3)*2 the domain is shrunk by a factor of two.
What is the effect of the number two in the function y = (x^3)/2 and y = (x^3)*2?
400
4*5 = 20 9^.632 * 9^.733 = 9^1.365
What is 9^x=20 given that 9^.632 = 4 and 9^.733 = 5?
400
a. log(2)20 + log(2)2 = log(2)40 b. log(2)4 + log(2)10 = log(2)40 c. log(2)5 + log(2)8 = log(2) 40
What are different ways to write log(2)40 as the sum of two logs?
500
Doing this to the y = x^2 function will make it possible for the function to have an inverse. In other words it will make the function one-to-one.
What is restricting the domain of the function?
500
If the original control points (0,1), (1,2), (2,4) and (3,8) are now (0,2), (1,4), (2,8), and (3, 16) then the function y = 2^x has been vertically stretched by a factor of two.
What is the transformation preformed on the function y = 2^x if the original control points (0,1), (1,2), (2,4) and (3,8) are now (0,2), (1,4), (2,8), and (3, 16)?
500
original function: y = √(1-x^2) function with domain and range expanded by a factor of two: y = 2√(1-x^2)/2
What is the transformation that increases both the domain and range of the semi-circle function by a factor of two?
500
4^2012 (4^3 - 4^2 - 4^1 +1) = 45(2^x) 4^2012 (45) = 45(2^x) 4^2012 = 2^x (2^2)^2012 = 2^x 2^4024 = 2^x x = 4024 32
What is x if 4^2015 - 4^2014 - 4^ 2013 + 4^ 2012 = 45(2^x)?
500
log(21)221 = log(10)221/log(10)21 log(21)221 = 1.77
What is the value of log(21)221? Use the change of base formula to find this value on your calculator.