Math Lesson 22

Solve the problems below. Write the problem, your work, and the solution in the text box below to submit your work. Be sure to show all of your work.

1 Given the function: f(x) = 3^x , a growth function. What are the domain and range?

2 Given the function:f(x) = (1 / 3 )^x,a decay function. What are the domain and range?

3 Given the function: f(x) = e^x . What is the equation of the asymptote? What does the asymptote tell you?

4 Given the function: f(x) = e^x . What are the intercepts?

B For each function, create T-chart (x values: -2, -1, 0, 1, 2) to find points to plot, then draw the graph. State the domain, range, intercepts, asymptotes, and end behavior. The graphs can be on desmos graphs. NOTE: If your y-values are too big to fit on the provided grid, adjust your y scale to accommodate those numbers.

5 f(x) = 2^(-2x) + 3

T-chart:

Domain:

Range:

Intercepts:

Asymptotes:

End behavior:

6 f(x) = .5^{(x - 1)}

T-chart:

Domain:

Range:

Intercepts:

Asymptotes:

End behavior:

7 j(x) =-2 (3/2)^x

T-chart:

Domain:

Range:

Intercepts:

Asymptotes:

End behavior:

8 g(x) = -e^x

T-chart:

Domain:

Range:

Intercepts:

Asymptotes:

End behavior:

9 f(x) =e^{(x + 3)}(HELP: e is approximately 2.7)

T-chart:

Domain:

Range:

Intercepts:

Asymptotes:

End behavior:

C Apply Your Knowledge

10 Refer to Ex 4 in the lesson content about bacteria growth.What is the end behavior for the bacteria? Explain what it means in this real life situation. Is there an asymptote? Why or why not? How many bacteria were present on Monday noon? How can you determine that from the graph?