Question

A clown at an amusement park makes animal shapes from twisted balloons. She sells each animal based on the number of balloons it requires, according to the following chart:
Numbers of balloons:

	$1$	$2$	$3$	$4$	$5$	$6$	$7$
Price:	4.00$	4.50$	5.00$	5.50$	6.00$	6.50	7.00$

Which of the following functions equals the dollar cost of a balloon animal that contains $x$ balloons?

• A. $f\left(x\right)=x$
• B. $f\left(x\right)=x+4$
• C. $f\left(x\right)=4x+0.5$
• D. $f\left(x\right)=0.5x+4$
• E. $f\left(x\right)=0.5x+3.5$

Answer 1

The correct option is E $f\left(x\right)=0.5x+3.5$

Checking each function if they satisfy the given values.
A. $f\left(x\right)=x$
Which means $f\left(1\right)=1$ which is not true
B. $f\left(x\right)=x+4$
Which means $f\left(1\right)=5$ which is not true
C. $f\left(x\right)=4x+0.5$
Which means $f\left(1\right)=4.5$ which is not true
D. $f\left(x\right)=0.5x+4$
Which means $f\left(1\right)=4.5$ which is not true
E. $f\left(x\right)=0.5x+3.5$
Which means $f\left(1\right)=4$ which is true
Thus, $f\left(x\right)=0.5x+3.5$ is the function which equals the dollar cost of a balloon animal that contains $x$ balloons.