Function or Not
Is this a function?
x | 1 | 2 | 3 | 4
y | 5 | 4 | 3 | 2
Yes, this is a function. For every one input (x), there is exactly one output (y).
The three most common representations for functions.
What are tables, equations, and graphs?
The function with the greater rate of change is ___.
Function A: y = 2x + 1
Function B: y = -3x - 5
What is function A?
The initial value of any proportional relationship
What is zero?
The slope of an increasing function.
What is positive?
Is this a function? (teacher will draw)
No, this is not a function. For the input (x=3), there are two outputs (y=1 and y=3).
Find the equation of the function from the table.
x | 0 | 1 | 2 | 3
y | 4 | 6 | 8 | 10
What is y = 2x + 4?
To compare functions in different representations, you look for these two properties.
What are the constant rate of change and the initial value (slope and y-intercept)?
What is y = 5x - 4?
What is a straight horizontal line?
Is this a function?
(1,0), (2,3), (2,3), (4,5), (6,10)
Yes, this is a function. For every input (x), there are exactly one output (y).
Use the equation y = 3x + 1 to fill out a table
x | 0 | 1 | 2 | 3
y | | | |
What is this?
x | 0 | 1 | 2 | 3
y | 1 | 4 | 7 | 10
Find the initial value of the function.
x | 1 | 2 | 3 | 4
y | 1 | 3 | 5 | 7
What is -1?
An online clothing company sells custom sweatshirts. The company charges $6.50 for each sweatshirt and a flat fee of $3.99 for shipping. Write a linear function in the form y = mx + b.
What is y = 6.5x + 3.99?
Interval 3 is doing this (teacher will draw)
What is decreasing?
To tell if an arrow model is a function, you look for this.
When there is only one arrow coming off of every input?
Mark has a $100 gift card to buy apps for his smartphone. Each week, he buys one new app for $5.
Write an equation that relates the amount left on the gift card, y, over time, x.
What is y = -5x + 100
The greater rate of change is in Function ___.
Function A: y = 8x - 2
Function B: x | 2 | 3 | 4 | 5
y | 4 | 7 | 10| 13
What is Function A?
A line has a slope of 6 and passes through the point (2,7). Write its equation in slope-intercept form.
What is y = 6x - 5?
Angela threw a ball of slime into the air. Sketch a function for the relationship between the height of the ball of slime over time.
Answers may vary.
1 - Nonlinear, increasing, positive slope
2 - Nonlinear, decreasing, negative slope
The ball will not bounce since it is slime
To tell when a graph is a function, you do this method.
What is the vertical line test (pencil test)?
Mark has a $100 gift card to buy apps for his smartphone. Each week, he buys one new app for $5.
Make a graph of this function.
Graph will be shown.
The greater initial value is in Function ___.
Function A: y = 8x - 2
Function B: x | 2 | 3 | 4 | 5
y | 4 | 7 | 10| 13
What if both functions have the same initial value?
A line passes through the points (4,19) and (9,24). Write a linear function in the form y = mx + b for this line.
What is y = x + 15?
Louis was walking his dog to the park. On the way, he had to stop to pick up his dog's waste, then continued on at a quicker pace due to the smell. Sketch a potential function.
Answers may vary.
1 - increasing, positive slope
2 - constant, zero slope
3 - increasing, positive slope