Evaluating Functions
Find h(1)
h(x) = (3x+2)^2
h(x) = (3(3) +2)^2 = 25
What is the domain / range of graph 1?
domain: (-inf, inf)
range: [0,inf)
What is f(1) in graph 1?
f(1) = 1
Write the equation of a transformed quadratic shifted left 3 and up 4
(x+3)^2 +4
What is f(g(2))?
f(x) = 4x + 3
g(x) = -x-2
g(2) = -(2) - 2 = -4
f(-4) = 4(-4) + 3 = -13
Find f+g(1)
f(x) = -3x+2
g(x) = 4x^2 + 2
f(1) = -3(1) + 2 = -1
g(1) = 4(1)^2 + 2 = 6
f+g(1) = 5
What is the domain of graph 2?
[-2, inf)
Find all values of x where f(x) = 4
x = 2 , -2
Write the equation of graph 2, the transformed square root function
sqrt(x+2)
What is f o g(x)?
f(x) = 2x+3
g(x) = x+4
f o g(x) = f(g(x) = 2(x+4) +3 = 2x + 11
Find f * g (x)
f(x) = x+2
g(x) = x - 3
f*g(x) = (x+2)(x-3) = x^2 - x - 6
What is the domain of graph 4?
(-inf, inf)
What are the intervals of increase on graph 3?
(-inf, -2) u (0, inf)
Graph the function is graph 1, reflected over the x axis
Upside Down Parabola (-x^2)
What is f o g(-2)?
f(x) = 12 / x
g(x) = x^2 +2
g(-2) = (-2)^2 + 2 = 6
f(6) = 12/6 = 2
What is f/g(x)?
f(x) = 2x+4
g(x) = x+1
f/g(x) = (2x+4) / (x+1)
What is the range of graph 4?
(-inf, 0]
For what values of x is f(x)>0 in graph 3?
(-3,0) u (0, inf)
Write the equation of the square root function (sqrt(x)) shifted right 3 and up 2
sqrt(x-3)+2
2 MUST BE OUTSIDE SQUARE ROOT
What is f(g(3)?
f(x) = 5 / x + 4
g(x) = 1 / (4 -x)
g(3) = 1 / (4-3) = 1
f(1) = 5/5 = 1
g(x) = x^2 + 4
f(x) = -2(x^2) + x
g(2) = 8
f(2) = -6
g - f(2) = 8 - (-6) = 14
What is the range of the absolute value function?
(Hint: Graph it)
range: [0,inf)
What are the intervals of decrease on graph 2?
N/A, square root functions is always increasing
Graph the following: -2|x-3|-2
Absolute Value Function: VS BAFO 2, Reflect over x axis, VT down 2, HT right 3
What is f(g(x)?
f(x) = x^2 -2
g(x) = 3x+1
f o g(x) = (3x+1)^2 - 2
(3x+1)^2 = (3x+1)(3x+1) = 9x^2 + 6x +1
f(g(x) = 9x^2 +6x - 1