Understanding functions

Cheryl was taking her puppy to get groomed. One groomer, Fluffy Puppy, charges a once a year membership fee of $120 plus $10.50 per standard visit. Another groomer, Pristine Paws, charges a $5 per month membership fee plus $13 per standard visit. Let f(x) represent the cost of Fluffy Puppy per year and p(x) represent the cost of Pristine Paws per year. 

Which equations should we use for f(x) and p(x) ?

• $f\left(x\right)=120+10.5x,\ \ p\left(x\right)=5+13x\ \$

• $p\left(x\right)=120+10.5x,\ f\left(x\right)=13+5x$

•  $f\left(x\right)=120+10.5x,\ \ p\left(x\right)=60+13x$ 

• $f\left(x\right)=120-10.5x,\ p\left(x\right)=13-5x$

The cost of Nate’s service is described by y = 4x + 6. The table shows the cost of Beth’s service. What is the distance between the y-intercepts of the two functions

• 4

• 6

• 8

• 10

Which quadratic function has the slowest rate of change?

• $y=x^2+3x+1$

• $y=2\left(x-3\right)^2+1$

• $y=-\frac{1}{2}\left(x+1\right)\left(x+2\right)$

• $y=4x+7$

Scoops, an ice cream shop, charges $2.50 per ice cream sundae. The price of an ice cream sundae at another ice cream shop is represented in the table.

• The price of an ice cream sundae at Scoops has a greater rate of change.

• The price of an ice cream sundae at Sundaes To Go has a greater rate of change.

• The functions have the same rate of change.

• Kay

• Jay

• They will have knitted the same number.

Mrs. Lugo and Mrs. Carroll sell balloon animals at different stands on the boardwalk. They each use a constant number of balloons per animal.

Mrs. Lugo started with a total of 300 balloons today, and she uses 5 balloons for each balloon animal she makes.

if both ladies used up all of their balloons, who made more balloon animals?

• Lugo

• Carroll

• they made the same amount

Consider the functions  $f\left(x\right)=3+10x$  ,  $g\left(x\right)=2^x$   and  $h\left(x\right)=5x^2$ .

Which function will have the greatest output when x=4

•  $f\left(x\right)$  

•  $g\left(x\right)$  

•  $h\left(x\right)$  

Consider the functions  $f\left(x\right)=3+10x$  ,  $g\left(x\right)=2^x$   and  $h\left(x\right)=5x^2$ .

Which function will have the greatest output when x=0

•  $f\left(x\right)$  

•  $g\left(x\right)$  

•  $h\left(x\right)$  

True OR False: All increasing exponential functions eventually exceed all increasing linear functions.

• True

• False

Which linear function has the LEAST rate of change?

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