Functions and Graphs
Function Operations
Domain
Rational Functions
Rational Inequalities
100
For graph 1: What is f(-1)?
0
100
If f(2) = 5 and g(2) = -16, what is (f+g)(2)?
-11
100
For graph 2, what is the domain?
[-2,4)
100
What is the domain of f(x) = x/(x+1)
{x| x is not -1}
100
What is the restricted values of f(x) = (x+1)/(x^2-4)? read x^2 as x squared.
{-2,2}
200
For graph 2: What is the range?
(-1,2]
200
If f(x) = 3x - 2 and g(x) = x + 1 What is (f - g)(x)?
(f - g)(x) = 2x - 3
200
For graph 1, what is the domain?
(- infinity, 2)
200
What is the inverse of f(x) = (x+2)/(3x-5). Bonus 300 points: Also find the range of f(x) :)
inverse function: f inverse = (-5x-2)/(1-3x) or equivalently = (5x+2)/(3x-1) Domain of f inverse = {x| x is not 1/3} Range of f(x) = {y | y is not 1/3}
200
What is the zeros of f(x) = (x^2+3x)/(x-5) Read x^2 as x squared
{-3,0}
300
For graph 1: For how many x values is f(x) = -1?
Twice. Once we can see at x = -3, and a second time we cannot see off the graph to the left because of the arrow.
300
If f(x) is graph 1 and g(x) is graph 2, what is (f - g)(1)?
0.5
300
If the domain of f(x) = (-1,5] and the domain of g(x) = [1,7) what is the domain of the product function?
[1,5]
300
For f(x) = 7/(x+2) and g(x) = (4x+1)/(x+2), what is the sum function (f+g)(x)? Also write its domain.
(f+g)(x)=4, with domain {x|x is not -2}
300
Based on the sign chart, when is the rational function greater then or equal to 0?
(-infinity, -5] U [1,2)
400
For graph 1: What is f(2)?
undefined because it is an open circle.
400
If f(x) is graph 1 and g(x) is graph 2, what is (f + g)(-2)?
1.5
400
If f(x) is graph 1 and g(x) is graph 2, what is the domain of (g/f)(x)?
[-2,-1)U(-1,2)
400
f(x) = 1/x and g(x) = 1/(x+1) find the difference function (g-f)(x). Also write its domain.
-1/(x^2 + x) read x^2 as x squared Domain = {x | x is not 0 and x is not -1}
400
According to the sign chart, when is the rational function less then 0?
(-5,-2)U(-1,1)U(2, infinity)
500
For graph 1: What is it's range?
(- infinity, 2]
500
If f(x) is graph 1 and g(x) is graph 2, what is the domain of (f+g)(x)?
[-2,2)
500
If the domain of f(x) is (-1,3] and the domain of g(x) is [-2,2], f(x) = 0 only when x = 2 and g(x) = 0 only when x = 1, what is the domain of (f/g)(x)?
(-1,1)U(1,2]
500
f(x) = (x+3)/x and g(x) = (x+2)/(x+1) find the quotient function (f/g)(x). Also write its domain.
(x^2+4x+3)/(x^2 +2x) Read x^2 as x squared. Can write not factored: [(x+1)(x+3)]/[x(x+2)] Domain: {x| x is not 0, x is not -1 and x is not -2}
500
For the function f(x) = (x+1)/(x-2) make a sign chart and determine when the function is less then or equal to 0.
[-1,2) Sign chart should have the numbers -1 and 2. zero written below -1, R.V. below 2. On the interval (-infinity, -1) it should be marked POS (+) On the interval (-1,2) is should be marked NEG (-) On the interval (2, infinity) it should be marked POS (+)
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