Algebraic functions powerpoint

PowerPoint Part I

1. Algebraic Functions Caron White EDU 290

2. What are Algebraic Functions? A function that involves only algebraic operations, like, addition, subtraction, multiplication, and division as well as fractional or rational exponents. y= is now f(x)=

3. Function Input Number inserted into the function. f(x)=x+7 f( 3 )= 3 + 7 This is known as Domain (x).

4. Function Output Number “spit out” of function. The outcome of an input. f( 3 )= 3 +7= 10 This is known as Range (y).

5. Functions With Same Output Different inputs can have equal outputs. This IS a function.

6. Is it a Function? One input has two outputs. This is NOT a function.

7. Ordered Pairs Points on a graph. Can be pulled from a table. {(2,6),(3,5), (5,7),(7,9)}

8. Vertical Line Test Only one point crosses. If two points=>not a function.

9. Linear Algebraic Functions A function that can be graphically represented in the Cartesian coordinate plane by a straight line. f(x)= mx+b

10. Solving for Linear Functions 27x+9y=18 solve for y -27x from both sides 9y=-27x+18 /9 on both sides y=-3x+2

11. Tables for Linear Functions Input values for x f(x)=-3x+2

12. Graphing Linear Functions f(x)= mx+b b is the y-intercept m is the slope x is any value (input)

13. Graphing Linear Functions Continued f(x)=-3x+2 Graph points from table

14. Is This a Linear Function ? 14x-28y=7 solve for y -14x from both sides -28y=-14x+7 /-28 on both sides y =(1/2)x-(1/4) Yes! Fractions can be constants!

15. Is This a Linear Function? +3y=12 solve for y + to both sides 3y=9 +12 /3 on both sides y=3 +4  

16. Continuation… y=3 +4 No! This is a Quadratic function! Quadratics are our next section.  

17. Citations Slide 2 Citation: Algebraic Functions: Definition & Examples. ( n.d. ). Retrieved from http:// study.com/academy/lesson/algebraic-function-definition-examples.html Slide 9 Citation: Linear Function. ( n.d. ). Retrieved from http:// www.icoachmath.com/math_dictionary/Linear_Function.html