Domain & Range
The domain of a function is made up of:
The range of a function is made up of:
x values, inputs
y values, outputs
Is it a function:
{{(2, 4), (3, 6), (1, 1), (6, 3)}}
Yes
Identify the vertex of the parabola:
y=(x-4)2 + 6
(4, 6)
Explain the process for graphing a piecewise function. Be sure to include the terms "equations" and "intervals" in your answer
First, you look inside the bracket to determine what the equations of the lines to be graphed are. Then, you look at the interval to determine where/how far on your x-axis you graph the line. Then, you graph each equation for its corresponding interval.
An absolute value function always looks like?
The letter V
State the domain and the range:
{{(3, 6), (-2, 5), (4, 1)}}
Domain: {{3, -2, 4}}
Range: {{6, 5, 1}}
Is it a function?
{{(1, 1), (2, 1), (3, 1), (4, 1)}}
Yes
A parabola has the equation y=(x + 3)2 -2 and is shifted to the right 3 units and down 6 units. Write the equation of the translated parabola in vertex form
y= x2 - 8
What do the inequalities in a piecewise function represent?
The intervals/domains for each function
Solve the absolute value equation for all values for x:
|x+12| = 7
x = -5
x = -19
State the domain and range:
{{(0, 4), (z, -1), (3, p), (-3, -9)}}
Domain: {{0, z, 3, -3}}
Range: {{4, -1, p, -9}}
Is it a function?
{{(2, 5), (3, 5), (2, 7), (6, 1)}}
No, the input 2 is repeated with a different output
Explain the transformation that happens from
y= (x - 1)2 + 4 to y= (x + 7)2 - 4
Shifted 8 units to the left and 8 units down
Graph the piecewise function:
y= 2x - 1 if x≤1
y= 3x + 1 if x>1
For y= 2x - 1 there is a closed circle on (1, 1) and an arrow on the other end going down and to the left
For y= 3x + 1 there is an open circle on (1, 4) and an arrow on the other end going up and to the right
The domain of a function is 2≤x≤7 and the range is 7<y≤12. Rewrite the domain and range in interval notation.
Domain: [2, 7]
Range: (7, 12]
Create a graph that has the domain 4≤x≤8 and the range 1≤y≤2
Closed circle at (4, 1), closed circle at (8, 2)
Is it a function?
{{(3, z), (w, 3), (2, 4), (5, z), (w, z)}}
No, the input w has two different outputs
Explain the difference between the parabolas
y = x2 -2 and y = -x2 -2
The first graph faces up and the second graph faces down. They both share the same vertex.
Graph the piecewise function:
y = 4 if 0≤x<2
y = 5 if 2≤x<4
y = 6 if 4≤x<6
For y=4 there should be a closed circle on (0, 4) and an open circle on (2, 4)
For y=5 there should be a closed circle on (2, 5) and an open circle on (4, 5)
For y=6 there should be a closed circle on (4, 6) and an open circle on (6, 6)
The domain of a function is (7, 12) and the range is [-3, 1). Rewrite the domain and range as compound inequalities
Domain: 7<x<12
Range: -3≤y<1
Create a graph that has the range -3<y≤2 and the domain -1<x<5
Open circle at (-1, -3), closed circle at (5, 2)
Gerald draws a vertical line through a graph. The line touches the graph at two different points. Is it a function? Explain
No, it is not a function because it doesn't pass the vertical line test (touches more than one point)
If (0, 3) is a point on the graph of y=f(x), which of the following points must be on the graph of y=f(x) + 5
A: (0, -2)
B: (5, 3)
C: (0, 8)
D: (-5, 3)
C: (0, 8)
Graph the piecewise function:
y= x + 6 if x ≤ -3
y= -2/3x - 3 if -3≤x<6
For y= x+6 there should be a closed circle on (-3, 3) and an arrow on the other end going down and to the left
For y= -2/3x -3 there should be a closed circle on (-3, -1) and an open circle on (6, -7)
These animals are a popular delicacy in Asia and are known to produce an substance that helps relieve arthritis
Sea slugs