Function graphs & looking at 3 types of functions.

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Presentation transcript:

Function graphs & looking at 3 types of functions

Explore worksheet

Let’s look at some applications…

Example: a car travels at a steady rate of 65 miles per hour. The number of miles the car travels is a function of the number of hours the car is driven at this rate. Write a function equation that models this function. f(x) = 65x or m(h) = 65h

Is this linear? How do you know? Evaluate f(3) What is the meaning of f(3)? Can you give an example of an evaluating problem that doesn’t make sense for this problem situation? f(x) = 65x

Example: the height of a flea jumping can be described as a function. The height of a flea is a function of the time after it starts to jump. The function equation for a particular jumping flea can be modeled with the equation: h(t) = -16t 2 + 6t t = time in seconds & h = height in feet

Jumping flea function h(t) = -16t 2 + 6t What type of function is this? How do you know? What does the graph of the function look like?

Jumping flea function h(t) = -16t 2 + 6t Evaluate this function for the following times: h (0.2) h (0.3) h (0.4) What statements can you make from the results you found?

The amount of money in a savings account is a function of the time (in years) the money is in the account. Brandon started with $500 and his account pays 5% annual interest. The function equation that models the amount of money in Brandon’s account is: A (t) = 500 (1.05) t

Brandon’s Savings Account Function: A (t) = 500 (1.05) t What type of function is this? How do you know? What does the graph of the function look like?

Brandon’s Savings Account Function: A (t) = 500 (1.05) t Where t = time in YEARS Evaluate this function for the following times (careful…) A (2 years) A (1 decade) A (18 months) A (-5) What statements can you make from the results you found?