End Behavior of Exponential Functions

Select all the exponential graphs that are decreasing towards zero on the left end of the graph.

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What is the domain and range of the exponential function shown?

• Domain all real numbers and range y > 1.

• Domain all real numbers and range y > 2.

• Domain all real numbers and range y < 2.

• Domain x > 2 and range y > 2.

Whats the horizontal asymptote?

• y=3

• y=-2

• y=-3

• (0,-3)

Whats the horizontal asymptote?

• (0,3)

• y=3

• y=-2

• y=2

What is the range of this graph?

How can you tell if

y = A * B^x

^{is a growth model?}

• B > 1

• B < 1

• B = 1

• A < 1

This graph models y = (0.2)^x - 3. Which statement describes what happens to the y value as x increases?

• As the value of x becomes very large, the value of y approaches - 0.2.

• As the value of x becomes very large, the value of y approaches -3.

• As the value of x becomes very large, the value of y approaches -2.

• As the value of x becomes very large, the value of y will gradually

  decrease to negative infinity.

Consider the equation 70(0.8)^x + 2. What is the end behavior of the function as x approaches infinity?

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A population of mutant venus fly trap plants are taking over an island in the South Pacific, capturing everything from insects to small rodents. When they were first discovered they covered 4 square kilometers. As the population grows, the plants spread and cover more land. How many years will it take for the plants to occupy 400 km²?

• 8 years

• 9 years

• 10 years

• 11 years

Consider the equation 70(0.8)^x + 2. What is the equation of the asymptote?

• y = 70

• y = 0.8

• y = 2

• y = 0.2