Key Features
The table below shows the average rain for each state in inches. Find the domain and range.
Hawaii ---> 70.3
Nevada --> 9.5
Louisiana --> 59.15
Mississippi --> 59
Domain: Hawaii, Nevada, Louisiana, Mississippi.
Range: 9.5, 59, 59.15, 70.3
What are the five ways of combining functions?
Addition, subtraction, multiplication, division, and composite.
Is the following an inverse relation?
(3, -1) and (3, -1)
No must be swapped.
(-1,3)
What is the difference between a rigid and nonrigid transformation?
Rigid leaves the size and scale and nonrigid distorts the shape.
Where in the real world do we see inverse functions?
Currency, weather conversions, language, any translation or conversion.
What are the three types of discontinuities?
Jump, removable, and infinite
What is another way of writing f(g(x))?
(f o g)(x)=
f of g of x
What does the horizontal line test prove?
It proves the function has an inverse.
Identify the transformations.
f(x)= -2|x| + 10
Reflection over x axis, vertical stretch by 2, and up 10
Using desmos graph the function below and determine the interval where the function is negative.
|x| - 6
(-6,6)
Give an example of a graph that does not pass the vertical line test and horizontal line test.
A circle, sideways parabola
Find g(f(-3))
f(x)= 2x -7 g(x)= 5x + 1
-66
Find the points determined by s= 0, 4
x= s2 + 10 y= -s
t= 0 (10, 0)
t= 4 (26, -4)
Identify the transformations.
f(x)= 0.25(-x + 10)3
Vertical compression by 0.25, reflection over y axis, and left 10
Find f(g(h(x))).
f(x)= 2x g(x)= x + 1 h(x)= x2
2x2 + 2
Using desmos graph the function below and determine the end behavior.
f(x)= x3 - 4
lim f(x) = ∞
x-> ∞
lim f(x) = -∞
x-> -∞
Find the new function g/f and the new domain.
f(x)= 2x g(x)= √x
√x/2x
domain: (-∞,0) u (0,∞)
Find and algebraic relationship between x and y.
x= t3 + 2t y= -5t
x= -y3/ 125 - 2y/5
x= (-y/5)3 + 2(-y/5)
Identify the transformations.
f(x)= (10x)3
Horizontal compression by 1/10
Confirm that f and g are inverses.
f(x)= x3 + 1 g(x)= cube root (x - 1)
f and g are inverses because
f((g(x))= x and g(f(x))= x
Algebraically determine whether the function is even, odd, or neither.
f(x)= x2 - 2x
Neither
Find f(g(x)).
f(x)= x2 + 2x - 5 g(x)= -2x
4x2 -4x -5
Algebraically find the inverse of the function.
f(x)= 2x3 + 10
y= 2x3 + 10
x= 2y3 + 10
x-10 = 2y3
(x-10)/ 2 = y3
cube root ((x-10)/2)
Identify the transformations.
f(x)= -7|1/4x - 5 | - 10
Reflection over x axis, vertical stretch by 7, horizontal stretch by 4, right 5, and down 10
What does the function of sin x look like? What is the domain and range?
Cyclical, domain all real numbers, range [-1,1]. Passes thru (0,0)