Systems
Lines
Am I a function?
Absolute Value Functions
Piecewise
100
What is the solution?
(-1,1)
100
What is the slope of y=2x+4?
What is m=2?
100
What is No, not a function? It does not pass the vertical line test.
100
What is the parent function to all absolute value functions?
f(x) = |x|
100
True or False: For a piecewise function, we would graph an open dot at x=-2 for a piecewise function with the following domain restriction:
x<=-2
False!
200
Solve the systems of equations (How many solutions?):
-8x + y = -7
16x - 2y = 14
Infinitely Many Solutions
200
What is the slope of y + 2x = 4
What is m= -2
Must get in Slope-intercept form first.
y = -2x + 4
200
What is Yes?
200
Identify and describe the transformation:
g(x) = |x| + 4
Vertical translation of four up
200
Given the piecewise function f(x), find f(5).
f(5)=13
300
Solve the systems of equations:
-5x - 5y = 10
y = -4x -17
(-5, 3)
300
What is the y intercept of y = -3x - 5?
b= -5
300
The mapping diagram shows a function or not.
What is No, not a function?
300
Identify the vertex of the following function and graph it.
y=2|x+5|-3
Vertex: (-5,-3)
300
Given the piecewise function f(x), find f(-10).
f(-10)=104
400
Graph the system of inequalities.
y >2
y < 2x - 4
Is (0,0) a solution to the system? Why?
No
400
What is slope of y=-3?
Zero slope
400
Does the following table represent a function?
x y
1 2
2 5
6 2
2 9
5 1
What is No, because the input (x) of 2 has two different outputs (y)?
400
What is the domain and range of the following function?
y= |x-3|+4
Domain: All real numbers
Range: y >= 4
400
True or False? Given the piecewise function f(x), at x=0 the two piecewise functions that share that domain will connect at the same point.
False!
500
A farmhouse shelters 10 animals. Some are pigs and some are ducks. Altogether there are 36 legs. How many of each pigs are there?
8
500
What is the slope of x = 2?
undefined
500
Is this a function and why?
What is no, because x's repeat at 8?
500
Find the vertex, axis of symmetry, domain and range of the following function and graph it
y = 1/3|x-1|-5
Vertex: (1, -5)
Axis of symmetry: x = 1
Domain: All real numbers
Range: y >= -5
500
A piecewise function is said to be "continuous" if there are no breaks or gaps in the line that is formed.
Is this piecewise function continuous?
Yes!
At x=1 both lines meet at (1,5).
At x=3 both lines meet at (3,1).