4. Let C(() represent the average price of gasoline in the United States, in dol

Question

4. Let C(() represent the average price of gasoline in the United States, in dollars per gallon, t years after Cody was born. A graph of C is shown below: 3.51 3.50 3.44 3.00 250 2.00 1.50 1.00 050 000t 1-44 5 10 15 20 25 30 (a) Trent was born six years after Cody. If T(t) represents the average price of gasoline in the United States, in dollars per gallon, t years after Trent was born,2 write a formula for T(t) (b) Sketch the graph of T (c) What does this problem tell us about the relationship between transformations of function formulas and transformations of function graphs?

Explanation / Answer

Since, Trent was born six years after Cody.

T(0) = C(6) . This is quite intuitive as after six years of birth of cody same things were happening as on birth of Trent.

Similarly we can conclude that. T(x) = C(x+6), (By above argument) ...................(a)

For the graph of T(x) simply shift the above graph left by 6 years, that is the 6 on the x axis becomes 0,

old X axis - 0 1 2 3 4 5 6 7 8 9 10 ...

new X axis- 6 -5 -4 -3 -2 -1 0 1 2 3 4... ..................(b)

This tells us that if we know the graph or function of F(x) then to plot the graph of F(x+a),

we need to shift the previous graph to the left by a units. for F(x-a) , shift right by a units.

Note: Coincide their origins, else reference would be changed. ....................(c)

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.