Domain & Range
How do you find the domain and range?
Domain= all x values the function is defined over.
Range= all y values the function is defined over.
Find the domain of f(x)= 2x-1 & g(x)= 2x2.
Domain of 2x-1 : All real numbers
Domain of 2x2 : All real numbers
Find the equation of the x-axis reflection of F(x)= x+ 2
x-axis reflection equation: F(x)= -x -2
Describe the transformation of the function: x2 + 5
The function will have a vertical translation of 5 units up.
Is the following a polynomial? x3 - 11x4 + 7
If so find the power and leading coefficient.
Yes it is a polynomial.
Power= 4 LC: -11
What does a close circle and open circle tell you about the domain or range?
Close circle= includes the point use a [
Open circle= does not include the point use a (
Find the formulas of the functions f x g.
f(x)= 2x-1 g(x)= 2x2
f x g= 4x3 - 2x2
Given the quadratic function in vertex form find the vertex: f(x)= (x+ 11)2 – 9
vertex: (-11, -9)
Describe the transformation of the function: (x-5)2 - 7
The function has a horizontal translation of left 5 and a vertical translation down 7.
Find the slope of the following points:
f(5)= 2 & f(7)= -5
Slope= -7/2
Define an asymptote.
A line that a curve approaches, as it heads to infinity.
Find the formula of the functions f/g.
f(x)= 2x-1 g(x)= 2x2
f/g= (1/x) - (1/2x2)
Draw a scatter plot that has no correlation.
A scatter plots with points everywhere no pattern and no correlation.
The horizontal stretch or shrink factor will affect the [blank] in a graphical transformation.
The horizontal stretch or shrink factor affects the whole function in a graphical transformation.
If f(0)= 1 and f(2)= -3 find the equation of the line.(Point slope form: y-y1 =m(x- x1))
y= -2x + 1
Find the domain and range of the graph on the board.
Domain: (-∞, -1) u [1, ∞)
Range: (-∞, 2) u [2, ∞)
Find f(x) and g(x) given f(g(x))= sin5x
f(x)= x5
g(x)= sin x
An S shape curve is not a [blank], but it does have an [blank]. This can be found by using the horizontal and vertical line test.
An S shape curve is not a [function], but it does have an [inverse].
The vertical stretch or shrink factor affects the [blank] in a graphical transformation.
The vertical stretch and shrink factor affects all the x term in a graphical transformation.
Find the vertex given the quadratic function in standard form: 2x2+ 8x - 3
vertex: (-2, -11)
Algebraically find the vertical and horizontal asymptote: (x2 + 4x + 3)/ (x+3)(x-7)
Vertical asymptote: x=7
Horizontal asymptote: y=1
Find f(x) and g(x), given f(g(x))= 36x2 + 12x + 2
f(x)= x2 + 2x + 2
g(x)= 6x
Find the equation of the origin reflection:
f(x)= -x5 - x3 + x + 6
f(x)= -x5 - x3 + x - 6
Describe the transformation of the function
y= -2|x- 5| + 8 and state the parent function.
Parent function = |x|
Vertical stretch of 2, reflected over x axis, vertical translation of 8 units up, and horizontal translation of 5 units right.
A ball is kicked from a hill of 12ft. After 15 seconds, the ball falls at a minimum height of 1ft. Find the vertex form of the quadratic equation that models the ball’s path. (f(x)= a(x-h)2 + k)
y= 11/225(x- 15)2 + 1