Advanced Algebra, 10.1 Operations and COmposition

Presentation

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Mathematics

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10th - 12th Grade

•

Hard

•

CCSS

HSF-BF.A.1B, HSA.APR.A.1, HSF-BF.A.1C

Standards-aligned

Jeremy Adelmann

Used 18+ times

FREE Resource

7 Slides • 10 Questions

Advanced Algebra,

10.1 Operations and Composition

By Jeremy Adelmann

Multiple Choice

Simplify.

$\left(x^2+1\right)+\left(3x+5\right)$

$x^2+3x+6$

$x^2-3x-4$

$3x^3+5x^2+3x+5$

$\frac{x^2+1}{3x+5}$

$x-\frac{5}{3}+\frac{25}{9x+15}$

Multiple Choice

Simplify.

$\left(x^2+1\right)-\left(3x+5\right)$

$x^2+3x+6$

$x^2-3x-4$

$3x^3+5x^2+3x+5$

$\frac{x^2+1}{3x+5}$

$x-\frac{5}{3}+\frac{25}{9x+15}$

Multiple Choice

Simplify.

$\left(x^2+1\right)\left(3x+5\right)$

$x^2+3x+6$

$x^2-3x-4$

$3x^3+5x^2+3x+5$

$\frac{x^2+1}{3x+5}$

$x-\frac{5}{3}+\frac{25}{9x+15}$

Multiple Select

Simplify.

$\left(x^2+1\right)\div\left(3x+5\right)$

$x^2+3x+6$

$x^2-3x-4$

$3x^3+5x^2+3x+5$

$\frac{x^2+1}{3x+5}$

$x-\frac{5}{3}+\frac{25}{9x+15}$

(f+g)(x) = f(x) + g(x)

= (x² + 12) + (3x - 7)

= x² + 12 + 3x - 7

= x² + 3x + 12 - 7

(f+g)(x) = x² + 3x + 5

Given f(x) = x²+ 12 and

g(x) = 3x - 7, find

(f+g)(x) = f(x) + g(x)

This simply means to add the two functions and combine like terms.

Addition:

Adding and Subtracting Functions

Please take notes on the above information.

(f-g)(x) = f(x) - g(x)

= (x² + 12) - (3x - 7)

= (x² + 12) +(-3x + 7)

= x² + 12 - 3x + 7

= x² - 3x + 12 + 7

(f+g)(x) = x² - 3x + 19

Given f(x) = x²+ 12 and

g(x) = 3x - 7, find

(f-g)(x) = f(x) - g(x)

For subtraction, change the signs of each term in the functions, Then combine like terms.

Subtraction:

Adding and Subtracting Functions

Please take notes on the above information.

Fill in the Blanks

Perform the indicated operation. (Use the carrot to indicate an exponent. For example, $x^2+8$ would be written as x^2 + 8.)

If $f\left(x\right)=-4x-1$ and $g\left(x\right)=x^2\ +\ x$ , find $\left(f+g\right)\left(x\right)$

Type answer...

Fill in the Blanks

Perform the indicated operation. (Use the carrot to indicate an exponent. For example, $x^2+8$ would be written as x^2 + 8.)

If $h\left(a\right)=a^2-3$ and $g\left(a\right)=3a+3$ , find $\left(h-g\right)\left(a\right)$

Type answer...

(f⋅g)(x)= f(x) ⋅ g(x)

= (x² -3x - 40)(x + 5)

= x²(x+5) - 3x(x+5) - 40(x+5)

= x³ +5x² -3x² +15x -40x -200

= x³ - 2x² - 25x - 200

(f⋅g)(x) = x³ - 2x² - 25x -200

Given f(x) = x²- 3x - 40 and

g(x) = x + 5, find

(f⋅g)(x) = f(x) ⋅ g(x)

For multiplication, multiply each term in the first function by each term in the second function (F.O.I.L). Then combine like terms.

Multiply:

Multiply and Divide Functions

Please take notes on the above information.

(f/g)(x)= f(x)/g(x)

= (x² - 3x - 40)/(x + 5)

= (x² - 3x - 40)÷(x + 5)

-5| 1 -3 -40

_____-5___40_

1 -8 | 0

(f/g)(x) = x - 8

Given f(x) = x²- 3x - 40 and

g(x) = x + 5, find

(f/g)(x) = f(x)/g(x)

For division, make a fraction with one of the functions over the other. You can use synthetic division to divide the numberator by the denomiator.

Divide:

Multiply and Divide Functions

Please take notes on the above information.

Fill in the Blanks

Perform the indicated operation. (Use the carrot to indicate an exponent. For example, $x^2+8$ would be written as x^2 + 8.)

If $g\left(n\right)=n-1$ and $h\left(n\right)=n^3-4$ , find $\left(g\times h\right)\left(n\right)$ .

Type answer...

Fill in the Blanks

Perform the indicated operation. (Use the carrot to indicate an exponent. For example, $x^2+8$ would be written as x^2 + 8.)

If $g\left(x\right)=-2x^2-5x-3$ and $h\left(x\right)=x-3$ , find $\left(\frac{g}{h}\right)\left(x\right)$ .

Type answer...

Example 1

(f⋄g)(x) = f[g(x)]

= 3( ) - 12

= 3(10x) - 12

= 30x - 12

(f⋄g)(x) = 30x - 12

Given f(x) = 3x - 12 and

g(x) = 10x find

(f⋄g)(x) = f[g(x)]

For the composition, start by writing the first function, with an open set of parenthesis instead of the variable. In the paraenthsis, write the other function.

Composition:

Composition of Functions

Please take notes on the above information.

Example 2

(g⋄f)(x) = g[f(x)]

= 10( )

= 10(3x - 12)

= 30x - 120

(g⋄f)(x) = 30x - 120

Given f(x) = 3x - 12 and

g(x) = 10x find

(g⋄f)(x) = g[f(x)]

This is the same as Example 1, but you start with second function and you plug in the first equation.

Composition:

Composition of Functions

Please take notes on the above information.

Fill in the Blanks

Perform the indicated operation. (Use the carrot to indicate an exponent. For example, $x^2+8$ would be written as x^2 + 8.)

If $f\left(x\right)=4x\ -\ 2$ and $g\left(x\right)=3x+4$ , find $\left(f\circ g\right)\left(x\right)$ .

Type answer...

Fill in the Blanks

Perform the indicated operation. (Use the carrot to indicate an exponent. For example, $x^2+8$ would be written as x^2 + 8.)

If $h\left(x\right)=x\ -\ 4$ and $g\left(x\right)=4x+3$ , find $\left(f\circ g\right)\left(x\right)$ .

Type answer...

Advanced Algebra,

10.1 Operations and Composition

By Jeremy Adelmann

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