1.1
When is a relationship NOT a function?
What is when a function has two or more outputs assigned to the same input?
If the cost in dollars of making x pounds of candy is given by the function
C(x)=10x+500.
Determine the cost of making 50 pounds of candy.
What is C(50)=10(50)+500= 1,000
Students who score within or including 20 points of the number 40 will pass a particular test. Write this statement using absolute value notation and use the variable x for the score.
What is 20<=x<=60?
Given f(x)=x-4 and g(x)= x^4 evaluate (f+g)(x)
What is x^4+x-4?
Define domain and range. What is the difference between them?
The domain is the values on the x axis and the input/independent variable. The range is the values on the y- axis and the output/dependent variable.
Is this a function? Why?
Inputs: 1, 2, 3, 4
Outputs: 1, 2, 3,4
What is yes, each input has only one output.
Find the domain and range of the function h(x)=sqrt(x).
What is
Domain: [0,infinity)
Range: [0, infinity)
Solve |x-8|=10.
What is x=2 and x=-18?
Define a composite function.
What is f(g(x)) where the set of those inputs, x, in the domain of g for which g(x) is in the domain of f.
A.K.A using f(g(x)) to match the function h(x)
The number of cubic yards of dirt, D, needed to cover a garden with area, a, square feet is given by the function D=g(a).
Explain the meaning of the statement g(3,000)=30
You need 30 cubic yards of dirt to cover a garden of 3,000 sqft.
Is this a function? Why?
Inputs: 1, 5, 3, 7
Outputs: 1, 3, 4, 4
What is no because there are two outputs associated with different outputs?
Find the domain and range of x^3+1.
What is
Domain:(-infinity, infinity)
Range: (-infinity, infinity)
Solve -|2x+3| +10 < 0.
What is -7/2<x<13/2
Given f(x)=2x+5 and g(x)=3-x^3 evaluate f(g(x))
What is -2x^3+11?
What is x= [ln(10)] / 2?
The number of cubic yards of dirt, D, needed to cover a garden with area, a, square feet is given by the function D=g(a).
The number of cubic yards of dirt needed to cover a garden is 100 yrd cubed when the area of the garden is 7,000 sqft. Express this information in terms of the function g.
What is 100yrd^3=g(7,000 sqft)
What is the domain and range of this function (x+1)/(4-x)?
What is
Domain: (-infinity, 4)U(4,infinity)
Range: (-infinity,-1)U(-1, infinity)
What is the vertical line test?
The vertical line test determines if the graph is a function. If it intersects with the function once then the graph is a function. If it intersects with the function more than once then it is not a function.
Use the function f(x)=4x+4 to evaluate the following.
[f(x+h) - f(x)] / h
What is 4?
Find the fixed cost in pounds? (When x=0)
Suppose the maximum cost allowed is $4,000. What are the domain and range of the cost of the function.
What is
Fixed cost: $3
Domain: [3, 3,997/4]
Range: [0,4,000]
What is n= 10/3 - 8p/3
Determine the domain and range of the function y=|x|
Domain: (-infinity, infinity)
Range: [0, infinity)
What is the horizontal line test?
Write h(x)=sqrt(4-x^3) as a composite function.
There are many answers to this question, but here is one
g(x)=4-x^3
f(x)=sqrt(x)
f(g(x)) is sqrt(4-x^3)
Find the domain and range of the function f(x)= sin(x).
Domain: (-infinity, infinity)
Range: [-pi/2, pi/2]