Functions
Linear Functions
Linear or Non-Linear Functions
Writing Linear Equations
Equations
100
What is a function?
Each input is assigned exactly one output.
100
What is the equation of this linear function?
It is y = (-1/3)x + 5
100
Does this graph represent a linear function?
Yes, it's a linear function!
100
In a linear equation, which variable represents rate of change?
The variable m.
100
A square has an area of 36 square feet. A second square has an area of 144 square feet. How much greater is the side length of the second square than the side length of the first square?
6
200
Does this table represent a function?
Yes, it's a function!
200
What is the equation of this linear function?
It is y = 4x + 6.
200
No, it's a non-linear function!
200
What is the slope of the line that passes through the points (-8,-6) and (4,3)
The slope is
+3/4
200
The equation y = 1,500 – 30x can be used to estimate the number of cars in a parking lot x minutes after the end of a concert. What is the meaning of the slope of the linear model?
About 30 cars leave the parking lot every minute after the concert ends.
300
What ARE the DOMAIN AND RANGE?
D: {1,2,3,4,5,6} R:{-1,0,1,2,3,6}
300
What is the use of The Vertical Line Test
to determine if a graph is a function or not
300
Without a graph, how do you determine if a function is linear or non-linear?
Calculate rate of change (or slope).
300
A line has a slope of 3 and goes through the point (0,6). What is the linear equation that represents this line?
The linear equation is y = 3x +6
300
What is the value of x in the equation shown below?
1/2(2x+6)=5x+15-3x
-12
400
Does this mapping (arrow) diagram represent a function?
Yes, it's a function!
400
Which linear function has the greater rate of change? What is the rate of change for each panda?
The table has a greater rate of change. Mochi has a rate of change of 4 lbs/week. Kappa has a rate of change of 3 lbs/week.
400
Does this table represent a linear function?
No, it's a non-linear function!
400
What is the linear equation for a line that runs through the points (3, 11) and (0, 7)?
It is y = (3/4)x + 7
400
What is the approximate distance between the points (–2, 7) and (4, –3)?
11.7
500
(-1, 3), (0, 2), (1, 1), (2, 0), (0, 3)
Does this set of ordered pairs represent a function?
No, it's not a function!
500
Which linear function has a greater initial value? What is the initial value for each panda?
The graph has a greater initial value. Mochi has an initial value of 1 lb. Kappa has an initial value of 2 lbs.
500
Does this table represent a linear function?
Yes, it's a linear function!
500
In a store, 6 comics cost $12.75, and 13 comics cost $19.75. What is the slope for the linear equation? What does the slope represent?
Hint: ''x'' is the number of comics, and ''y'' is the total cost.
1) Slope = 1
2) The slope represents the cost per comic book
500
Two companies sell shirts. x The first company charges $18 per shirt plus an additional $12 for shipping. x The second company charges $20 per shirt plus an additional $4 for shipping. How many shirts are in an order that would cost the same from both companies?
4