Function Transformations
Combining Functions
Inverses
Function Writing
100
Vocab; what is a, if a>1:
g(x) = f(ax)
What is horizontal compression?
100
In the following equation, which function is input first: h(g(x))?
What is g(x)?
100
Find the inverse of the function: f(x) = 2/x+3
What is
f-1(x) = 2/(x-3)
100
Write a piecewise function for the graph:
x , x < -1
f(x) = { x2 + 1, -1 < x < 2
-1, x > 2
200
The graph of the inverse is always a reflection of the original graph over the line ______.
What is y=x?
200
f(x)=4x-3 g(x)=x^2+1 What is g(f(2))?
What is 26?
200
Find the inverse of the function:
g(x) = 0.5√(x - 5) + 3
What is;
g-1(x) = (2x - 6)2 + 5
200
Determine the equation for the line of best fit for the data: round to the nearest tenth.
y = 61.9x - 1.8
300
Identify the x-intercepts of g(x):
f(x) = x2 - 16
g(x) = f(2x)
(2, 0) and (-2, 0)
300
Given the functions:
h(x) = 5x+20
g(x) = 4/x
Determine the domain of g(h(x))
all reals, except for x=-4
300
Find f-1(x):
f(x) = 2x2+12.
f-1(x) = ±√(x/2 - 6)
300
The cost of renting a mountain bike is $25 for the first 3 hours and $5 for each additional hour, to a maximum of $60 a day. Write a piecewise function to represent the cost of renting a mountain bike for 0 to 24 hours.
must include for middle values:
25 0<x<3
5(x-3)+25, 3<x<10
60 10<x<24
400
4lx+2l-5
What transformations have been done to this equation?
What is vertical stretch by 4, left 2, and down 5?
400
Determine g(f(x)):
f(x)=x^2+1
g(x)=2-x
g(f(x)) = 1 - x2
400
Determine the inverse:
f(x) = 2x/3 - 5
f-1(x) = 3log2(x+5)
400
Determine the domain and range of the inverse of the function graphed:
Domain: all real numbers
Range: -pi/2 < y < pi/2
500
Determine the new function for g(x) in standard form.
Given that f(x) = x2 + 5, and g(x) is the following transformation on f(x): a horizontal compression of 2 and translation left 3.
g(x) = 4x2 + 12x +14
500
Compose the function from the parent functions:
f(x) ∘ g(x)
f(x) = log3(x)
g(x) = 9x
f(x) ∘ g(x) = 2x
500
Determine f-1(x); Write the answer in standard form
f(x) = 5
√(x) - 1
f-1(x) = x2 + 10x + 25
x2
500
Identify the best regression for the table.
Determine the equation for the regression you chose: round to the nearest tenth.
Quadratic:
y= -0.1x2 + 6.7x - 18.3