Find the domain and range of the relation:
{{0,6} , {1,5} , {2,4} , {3,3}}
D: {0, 1, 2, 3}
R: {3, 4, 5, 6}
100
What is the formula to find the average rate of change of a function f(x)?
(f(b)-f(a))
________
(b-a)
100
Describe the transformation of the parent function f(x) = | x | if g(x) = | x - 3 |
The graph of the parent function shifts 3 units to the right.
100
What function is formed when you compose f(x) with it's inverse?
The identity function, or, p(x) = x.
100
What are two ways that we can write "plug the function g(x) into f(x)"?
f(g(x)) or (f º g) (x)
200
Is the graph of the unit circle (x^2 + y^2 = 1) a function? Explain why or why not.
No it is not a function, if you graph a circle it will fail the vertical line test.
200
Given the interval of [-3,4] for the function g(x), state, but do not solve for the average rate of change of g(x) over this interval.
g(4) - g(-3)
__________
7
200
If the parent function is f(x) = x^2 , state what geometric transformation(s) can describe the graph of g(x) = 3x^2 - 6.
The geometric transformation could be a dilation of scale factor 3 and a translation 6 units down.
200
What is the inverse of f(x) = 23x?
The inverse is x/23
200
If f(x) = 2x and g(x) = x + 3 determine g(f(x))
g(f(x)) = 2x + 3
300
When is a function considered one-to-one? What method do we use to test if a function is one-to-one?
A function is considered one-to-one if every x-value corresponds to exactly one y-value. We use the horizontal line test.
300
Use the following table:
x | 1 | 3.8 | 4.7 | 9.00 | 13.8 | 12.00 |
y | 3 | 5.1 | 8.7 | 15.8 | 25.1 | 30.16 |
Find the average rate of change from [5.1, 25.1]
1/2
300
Use the following description of a transformation of the parent function p(x) = | x | to state the function g(x) after the transformation from p(x).
The graph is translated 6 units left and 3 units up.
g(x) = | x + 6 | + 3
300
Find the inverse of the function f(x) = (x + 3)/5
The inverse is 5x-3
300
If f(x) = x + 3 and g(x) = 2x + 3, determine the function h(x) that is defined as (g ° f) (x)
h(x) = 2x + 9
400
State the domain and range of the function f(x) = x^2
D: { -inf <= x <= inf }
R: {0 <= y <= inf }
400
If g(x) = 0.05x^2 - 1.3x + 22.8
Find the average rate of change for the interval [13,23]
-1/2
400
Use the following description of a transformation of the parent function p(x) = | x | to state the function g(x) after the transformation from p(x).
The graph is reflected over the x-axis and translated 3 units up
g(x) = -|x|+3
400
Show that the functions f(x) = (2x+4)/4 and g(x) = (4x-4)/2
Show your work to get y=x
400
If m(x) = | 3x + 5 | + 3, determine possible f(x) and g(x) that could have composed to become m(x).
Answers will vary. Examples include, f(x) = |x| + 3 and g(x) = 3x + 5 for f(g(x)).
500
Find the roots of the function x^2 + 2x - 3
{ 1 and -3 }
500
The total cost in dollars to produce x items can be represented by the function c(x) = 0.0003x^3 + 0.14x^2 + 12x +1400. Find the average rate of change of the total cost when the number of items changes from 200 to 400.
The average rate of change is 180 items
500
Use the following description of a transformation of the parent function p(x) = | x | to state the function g(x) after the transformation from p(x).
The graph is translated 5.5 units right and 4 units down, reflected over the y-axis and dilated by a scale factor of 2
g(x) = 2|-x - 5.5| - 4
500
Does y=x^2 have an inverse function if the domain is the set of all real numbers? Justify your answer. If not, what would need to occur for y=x^2 to have an inverse?
No, the inverse of x^2 should be sqrt(x). However, sqrt(x)'s domain and range is only 0 <= x <= inf and 0 <= y <= inf respectively.
500
Are compositions always commutative? For example, does f(g(x)) = g(f(x))? Give an example to show whether or not you're correct.
No, for example, if f(x) = | x | and g(x) = 3x, then g(f(x)) = 3|x| and f(g(x)) = |3x| which are not the same.