I Am Transformed!
I.
Suppose a basketball player named Henry is standing on the free throw line and
attempts to make a basket, wanting “nothing but net”. Unfortunately, he misses.
He does this over and over, always making the same exact mistake. His friend
Rosa notices that his shot can be represented by the function v = f(h) where v is
the vertical distance in feet the ball travels and h is the horizontal distance in feet
the ball travels. After looking at the graph, Henry starts to conjecture what he
would need to adjust to be successful (nothing but net).
A. What adjustment did Henry make if the expression was f(h) +2? Sketch a
graph of f(h) and f(h)+2 and explain why you think the graph would be
adjusted in this way.
B. What do you think the adjustment would be if the expression was f(h +2)?
Again, sketch a graph and explain how this adjustment is made.
Match each story below to one of the expressions at the right:
Matching
Function
Number
Situation
Rosa figured out that Henry needed to
try standing three feet closer to the hoop
just to see if he could make the basket.
Henry suggested that he stand on a stack
of books three feet high to make himself
taller.
Rosa said to increase the arc of his
throw to be three times as high.
Function
1) v= 3f(h)
2) v= f(h) + 3
3) v= f(h +3)
II.
Suppose every day I take a taxi around town. The trip is x miles, so the cost for
the trip is C = f(x).
Match each story to a function which represents the amount paid to the taxi driver.
Matching
Function
Number
Situation
I received a raise yesterday, so today I
gave my driver a five dollar tip.
I had a new driver today and he got lost.
He drove five extra miles and charged
me for it.
I haven’t paid my driver all week.
Today is Friday and I’ll pay what I owe
for the week.
The meter in the taxi went crazy and
showed five times the number of miles I
actually traveled.
III.
Function
1) C = 5f(x)
2) C = f(x) + 5
3) C = f(5x)
4) C = f(x + 5)
Suppose y = P(t) is a function that gives the population of the Salt Lake valley in
thousands of people, where t is in years from today. Write an expression that
would represent each of the following statements:
A. The population 20 years before today.
B. Twenty thousand more people live in Salt Lake City than we have today.
C. Twenty percent of the population we have today.