1. Warm-up
1) Find 2f(x) + 3g(x)
2) Find g(x) – f(x)
3) Find f(-3)

2. Temperature (degrees)
You are staying at a hotel that has a hot tub. The clerk forgot to make sure it was heated up. Right now the temperature is 70 degrees. The clerk says that it will get 10% warmer every hour.
1. When will the temperature be at least 103 degrees? In this context, will the function be discrete or continuous? Write the equation.
Time (hrs.)
Temperature (degrees) 1 2 3 4 5 6

3. Homework Check

4. Comparing Functions
You MUST write a sentence comparing the two things.
Just because you can do the math does not mean you understand it.
Comparing is showing understanding.

5. Comparing Intercepts
When you compare y-intercepts, you are comparing start points.
Just make a note of which function starts at a higher/lower value.
When you compare x- intercepts, you are comparing where they hit the x-axis.

6. Comparing Rate of Change
When comparing two linears, you can just compare their slopes.
When comparing two exponentials or comparing an exponential and a linear, you will have to find the rate of change for a given interval and then compare.

7. Linear and Exponential Stories

8. Which function increases faster, f(x) = 4x – 5 or g(x) = 4x – 5?-3 -2 -1 1 2 3 x
g(x) = 4x - 5 -3 -2 -1 1 2 3

9. Lena has been offered a job with two salary options.
The first option is modeled by the function f(x) = 500x + 31,000, where f(x) is her salary in dollars after x years.
The second option is represented by the function g(x) = 29,000(1.04)x, where g(x) is her salary in dollars after x years.
If Lena is hoping to keep this position for at least 5 years, which salary option should she choose? Support your answer by finding the rate of change over the first 5 years.

10. Write your own story to match each of the following functions:
1. 2.

11. Homework