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

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? 2. In this context, will the function be discrete or continuous? 3. Write the equation. Time (hrs.) Temperature (degrees)   1 2 3 4 5 6

Homework Check

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.

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.

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.

Linear and Exponential Stories

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

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.

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

Homework