Linear and exponential functions

Linear and exponential functions

1. WELCOME

2. Linear and Exponential F unctions Prepared by Motivational Shining Stars

3. Function A function is a Mathematical process that uniquely relates the value of “one variable” to the value of “one (or more) other variables.” Examples: ( ) , , , ,   Function Y=f(X) Output variable “Y” Input variable “X”

4. What Does Linear Mean? Linear come from the Latin word LINEARIS which means “Created by lines” If a graph is linear it will form a “Straight” A linear function is a function of the form: f(x)=mx+b Where, m and b are the real numbers and m≠ Linear expressions consist of only One variable and no exponents.   Straight line

5. Examples: y= 2 5 x+1 y=4(3/5)ⁿ Because of the variable as exponent. Transform the following into the form y=mx+b x+y=2 ; y=-x+2 -3x+2y=6 ; y=-1.5x+3 Slope of Linear Function Slope =   Linear function Non linear function

6. Expressions of L inear Function Standard: Ax+By=C Point Slope: y-y1=m(x-x1) Slope intercept: y=mx+b Slope: y=  

7. Graphing Linear Functions Using Points Use two points (x,y) and (x1,y1) Find these points on the graph For example, Let (x,y)=(1,2) a nd (x1,y1)=(3,4)

8. Exponential Function A function is called an exponential function if it has “a Constant Growth Factor” This means that for a “Fixed” change in (x,y) gets “Multiplied” by a fixed amount. An exponential function is a function of the form y= Where a≠ , b and and the “ exponent must be a variable.”   Remember that  

9. Exponential Function   Exponent P ower Base (n times)  

10. Indices Rules:   

11. Examples = =  

12. Graphs of Exponential Function Let’s examine Exponential Function. They are different then any of the other types of function we have studied because the “Independent variable” is in the exponent.   3 8 2 4 1 2 1 -1 1/2 -2 1/4 -3 1/8 3 8 2 4 1 2 1 -1 1/2 -2 1/4 -3 1/8   E xponent Base

13. Difference between Linear and Exponential Function Linear Function Linear functions change at “a constant rate per unit interval”. Exponential Function Exponential functions change by “a common ratio over equal intervals.” 1 2 2 4 3 8 4 16 1 2 2 4 3 8 4 16 1 2 2 4 3 6 4 8 1 2 2 4 3 6 4 8

14. IS THE EXAMPLE OF LINEAR OR EXPONENTIAL? Sebastian deposits $500,000 in a local bank that will pay out 5% interest every year. Is this example linear or exponential? A certain type of corn grows at the rate of 3 inches per week. Is t his example linear or exponential? The Munn Sugar processing plant is able to process 10 tons of sugar per month Assuming that this process stay steady. Is this example linear or exponential? Exercise biologist, Samantha discovered that to reduce soreness people should start biceps curls at 10 pounds. Then, progress weekly to 11 pounds, 14 pounds, 20 pounds, 32 pounds, 50 pounds and so on . Is this example linear or exponential?

15. Use of Linear and Exponential Functions in our life Use of Linear F unction Variable costs Rates Budgeting Making predictions Use of Exponential Function Putting money in saving account Student loans Radioactive decay

16. Conclusion Linear and exponential functions are the mathematical process for solving the problems of algebra . These functions plays very important role in Maths and also our real life. By using these functions, we can present our problems graphically . Basically , these are the base of Algebra and Mathematics.

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