## Determining and Predicting the Rate of Change of Functions

#### Aligned To Common Core Standard:

**High School Interpreting Functions** - HSF-IF.B.6

How to Predict the Rate of Change of Functions - Functions have extensive usage in advanced mathematics and calculus. Calculus is used extensively in other aspects of science. By definition, a function is a procedure in which every input gets associated with only one output. One of the implementations of the function is finding out its rate of change. A rate of change describes the change in one quantity about the other. In other words, if y is the independent variable and x is the dependent one then rate of change= (change in x )/(change in y) There are numerous parameters in which the rate of change of functions can be used comprehensively. Such as finding out the acceleration of a vehicle. The acceleration deals with the change in velocity concerning time. In general, the change in the rate of a function can be denoted as f(x)= (f(x+h) - f(a)) / (b-a ). This is a wonderful selection of worksheets and lessons that show you how to predict the possible rate of change of various functions.

### Printable Worksheets And Lessons

- Starting with Slope
Step-by-step Lesson- This is more of a basic reminder of the
skills that will be required for the other sections.

- Guided Lesson
- I know that it is a pretty lame scenario with the potatoes. I
was running low on creativity that day.

- Guided Lesson Explanation
- I always like to encourage students to draw a graph even if all
they needed was to calculate the slope.

- Practice Worksheet
- Some of the word problems might stump kids. That is why it gets
them into a set routine to adapt to the problem.

- Matching Worksheet - Many people will trip up between choices d and e.

#### Homework Sheets

Finding the slope on the first two leads us to finding an average trend on the third homework.

- Homework 1 - Slope is basically a measure of how fast a line ascends or descends.
- Homework 2 - The formula of slope is: y2 - y1 / x2 - x1
- Homework 3 - Mack had 4 kg Onions. He peeled 3 kg of them in 1 hour. Now he has 1 kg Onions left. The graph below shows Mack's situation.

#### Practice Worksheets

Now we have students start to interpret the meaning of the slope of the line.

- Practice 1 - Find the average rate of change of y with respect to x over the interval [11, 12].
- Practice 2 - To find the average rate of change put the interval values in equation and solve them.
- Practice 3 - Mary had 6 liters of milk in his jug. She was making milk shake at the rate of 3 liters of milk shake in 2 hours. He had 3 liters of milk left. The graph shows Mary's situation.

#### Math Skill Quizzes

We start with some simple word problems to target the concept of slope.

- Quiz 1 - A wall is 7 feet tall. After 2 years it was 9 feet tall. What does the slope tell us about the tree's growth situation is this negative or positive?
- Quiz 2 - A building was 100 feet tall. After 4 days construction was done and it was 150 feet tall. What does the slope tell us about the building growth situation is this negative or positive?
- Quiz 3 - Maria has 16 kg fresh fruits. After 2 hours she left with 8 kg fresh fruits. If an equation were written to represent this situation, what does the slope tell us about the growth of Maria's fresh flower is this negative or positive?