FUNction / LINEar ?
Which test is used to verify if an equation is a function?
Which test is used to verify if it is linear?
Various answers possible:
Function - vertical line test / 1 output for every input
Linear - constant rate of change / graph is a straight line / simplified down to y=mx+b
What are 3 different ways to say slope
Rise over run, Slope formula, rate of change, M
Describe the Transformation: (type, direction, value)
y=f(x)+8
It is a vertical translation up 8 units.
Name two of the fundamental properties of Absolute Values (there are 4 total)
|x| = |-x| ... |x| >= 0
|x*y| = |x| * |y| ... |x/y| = |x| / |y|
Is this a function? Is it linear?
y = -x + 3
Yes & Yes ... it is a linear function
Find the slope:
(3,6) ; (4,2) ; (5,-2)
Slope = (6-2) / (3-4) = (4)/(-1) = -4
Find 3 unique solutions using intercepts for: 1800=25x+15y
(0,120) ; (72,0) ; (60,20) ; (36,60) ; (12,100)
List the steps for solving an Absolute Value Equation (4 basic steps)
1. Isolate Absolute Value
2. Make sure it does not = -#
3. Set up 2 equations ... = +# & = -#
4. Plug solutions back in
Give an example of a continuous domain and a discrete domain ...
Find the slope:
y = 8 + 15x
Slope = 15
Describe the Transformation: (type, direction, value)
y=f(x+4)
It is an horizontal translation LEFT 4 units
Describe in words AND graph -8 < x < 18
X is less than 18 AND greater than negative 8.
Open circles on -8 & 18, shaded between
Is the graph of a Circle a function, why or why not?
No. It does not pass the Vertical Line Test ... crosses the line twice.
14x - 7y = 28
Provide a table with 3 points & describe in words a realistic scenario for f(x)=30-3x
ex) You start with $30 and are renting games that cost $3 each.
ex) You are 30 miles from home and travel 3mph.
(0,30) ; (1,27) ; (2,24) ....
Describe in words AND graph: y > 9 or y <0
Y is greater than 9 OR less than 0.
Open circles on 9 and 0; shaded to the outside
Is 8x - 4y = 16 a function? If so, is it linear?
Yes and Yes ... it can be simplified down to y=mx+b
Find the slope of the line y=-5
**Take your time and think through it**
Since it is a horizontal line, the y's never change, thus the slope = 0
Describe the Transformation: (type, direction, value)
y=f(-x)
It is a refection across the y axis
Solve:
-2 |x+4| + 8 > 20
NO SOLUTION ...
after step 1, you have |x+4|<-6