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Lesson 1 Winner, Winner Develop Understanding

Ready

Describe the transformation of each function from . Then write the equation of the function.

1.

a parabola opening up with the points (-3,3), (0,-6), and (3,3) graphed on a coordinate plane representing the transformation of the function f of x = x squared x–5–5–5555y–5–5–5555000

Description:

Equation:

2.

a parabola opening up with the points (-2,2), (0,-5), and (2,2) graphed on a coordinate plane representing the transformation of the function f of x = x squared x–5–5–5555y–5–5–5555000

Description:

Equation:

3.

a parabola opening up with the points (-5,4), (-3,0), and (-1,4) graphed on a coordinate plane representing the transformation of the function f of x = x squared x–5–5–5y555000

Description:

Equation:

4.

a parabola opening down with the points (0,-5), (2,-1), and (4,-5) graphed on a coordinate plane representing the transformation of the function f of x = x squared x555y–5–5–5000

Description:

Equation:

5.

a parabola opening up with the points (-5,4), (-3,2), and (-1,4) graphed on a coordinate plane representing the transformation of the function f of x = x squared x–5–5–5y555000

Description:

Equation:

6.

a parabola opening down with the points (-5,1), (-3,5), and (-1,1) graphed on a coordinate plane representing the transformation of the function f of x = x squared x–5–5–5y555000

Description:

Equation:

Set

Sofia is celebrating her Quinceañera. Isabella knows the perfect gift to buy Sofia, but it costs . Isabella can’t afford to pay for this on her own, so she is going to ask some friends to join in and share the cost.

7.

Write the function that models this situation. Define the meaning of each part of the function as it relates to the context of the story.

8.

Each statement gives information about the number of people donating or the amount of each equal donation. If the donation is given, find how many friends donated. If the number of friends is given, find the amount of the donation.

a.

Each friend donates .

b.

friends donate an equal amount.

c.

Each friend donates .

d.

The number of friends is the same as the number of dollars each donates.

e.

Enough people donate that each person only gives .

f.

Each friend donates .

g.

Only people donate money for the gift.

9.

Use the data from the statements to make a table showing the number of people and the amount each person donates.

Number of Friends Who Donate

Amount of Each Donation in Dollars

10.

Use the data in the table from problem 9 to make a graph of this situation.

a blank coordinate plane100100100200200200300300300400400400500500500100100100200200200300300300000

Go

11.

Match the function rule with the correct graph. Then write the equation of the horizontal asymptote. (Note: All exponential functions have a horizontal asymptote.)

a.

  1. ___

  2. ___

  3. ___

  4. ___

  5. ___

  6. ___

  1. a curved line representing an exponential function with a point at (0,4) and a horizontal asymptote at 3x–5–5–5555101010y555000
  2. a curved line representing an exponential function with a point at (0,-44) and a horizontal asymptote at -3x–10–10–10–5–5–5y–5–5–5000
  3. a curved line representing an exponential function with a point at (0,1) and a horizontal asymptote at 0x–5–5–5y555000
  4. a curved line representing an exponential function with a point at (0,-1) and a horizontal asymptote at 0x–5–5–5y–5–5–5000
  5. a curved line representing an exponential function with points at (3,1) and (5,4) a horizontal asymptote at 0x555y555000
  6. a curved line representing an exponential function with a point at (0,-2) and and a horizontal asymptote at -3x–10–10–10–5–5–5y000

b.

Write the equation of the horizontal asymptote for each of the equations.

Equation

Horizontal Asymptote

12.

Use to explain which values affect the position of the horizontal asymptote in an exponential function. Be precise.

13.

Why does an exponential function have a horizontal asymptote?