Introduction to Functions

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.

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.

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

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

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)

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 graph is a function of x?

B

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.

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.

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.

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

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.

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 equation is a function of x?

X^2=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.