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Introduction to Functions

Terms in this set (17)

The graph below models the value of a $20,000 car t years after it was purchased.

Value of Car

mc020-1.jpg

Which statement best describes why the value of the car is a function of the number of years since it was purchased?
Each time, t, is associated with exactly one car value, y.
Jada fills the bathtub before taking a bath and then allows the water to drain when she is done. The graph below models the number of gallons of water, y, in the bathtub over time, t, in minutes.

mc021-1.jpg

Is the number of gallons of water in the bathtub a function of time?
Yes because each t value is paired with exactly one number of gallons.
Lorraine writes the equation shown.

es027-1.jpg

She wants to describe the equation using the term relation and the term function.

The equation represents
a relation and a function
The temperature in degrees Celsius, c, can be converted to degrees Fahrenheit, f, using the equation mc026-1.jpg. Which statement best describes the relation (c, f)?
It is a function because every Celsius temperature is associated with only one Fahrenheit temperature.
The table below lists some of the characteristics of the houses on Katrina's street.


Characteristics of Homes For Sale on Katrina's Street
Bedrooms
Acres of land
Sale price
Appraised value
Property tax
2
0.17
$230,000
$200,000
$1,220
2
0.20
$210,000
$220,000
$1,232
3
0.20
$275,000
$250,000
$1,400
4
0.24
$275,000
$275,000
$1,540
4
0.52
$360,000
$310,000
$1,736
4
0.75
$350,000
$320,000
$1,792
5
1.23
$375,000
$350,000
$1,960

Which relationship describes a function?
(appraised value, property tax)
Which equation is a function of x?
X^2=y
A company has determined that its weekly profit is a function of the number of items that it sells. Which equation could represent the weekly profit in thousands of dollars, y, when the company sells x items?
y=-x^2+50x-300
Which graph is a function of x?
B
Removing which point from the coordinate plane would make the graph a function of x?
(-2, 1)
Removing which ordered pair from the table would make the relation a function of x?
(4, 1)
3 5 7 9 10
...
The chart below lists the original and sale prices of items at a clothing store.

Clothing Prices
Original price
Sale price
$7.99
$5.59
$10.99
$7.69
$12.99
$9.09
$15.99
$11.19
$24.99
$17.49
$29.99
$20.99

Which statement best describes why the sale price is a function of the original price?
For every original price, there is exactly one sale price.
Which statement describes how to determine if a relation given in a table is a function?
If none of the input values are repeated, the relation is a function.
Which statement best illustrates using the vertical line test to determine if the graph below is a function of x?
The graph is not a function of x because the line x = 0 intersects the graph at two points.
Which statement is a correct interpretation of the vertical line test?
If any vertical line can intersect the graph at more than one point, the graph does not represent a function.
The equation below models the height in feet, h, of a softball t seconds after it is hit by a batter.

mc023-1.jpg

Why is the height of the ball a function of time?
Each value of time is associated with exactly one height.
Hal, Zelda, Maya, and Jason each recorded the height and age of five classmates. They used the data to create the tables below.

mc022-1.jpg

In which student's data can height be considered a function of age?
Hal
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