Thursday 1.28 Alg 2 Combining Functions

Thursday 1.28 Alg 2 Combining Functions

Warm Up!

You will need scratch paper for your warm up!

Multiple Choice

Factor by GCF:

10a⁴+16a+10a²

• 2a(5a³⁺8+5a)

• 2a⁴(5a+8a²+5a³)

• 2a⁴(10+16a+40a²)

• 3a³(5+8a+a²)

Multiple Choice

Factor by Grouping:

20x³-25x²+4x-5

• (5x²-5)(4x+1)

• 5(x²-1)(4x+5)

• (5x²+1)(4x-5)

• (5x²+1)(4x-1)

Finding GCF when leading coefficient is negative:

• If the leading coefficient of a polynomial is negative, the GCF should be negative as well.

• For Example   $-2a^3-4a^2=-2a^2\left(a+2\right)$  *the GCF is negative. Notice how the signs change for remaining binomial. 

Multiple Choice

2x³-8x²-x+4

• (2x²-1)(x-4)
• 2(x²-1)(x+4)
• (x²-1)(2x-4)
• (2x²+1)(x-4)

Multiple Choice

Factor by grouping
x³ - 4x² -4x + 16

• (x+4)(x+2)
• (x-4)(x² -4) 
• (x+4)(x² -4)
• (x-4)(x-2)

No Need to Take Notes

The Next 4 Slides are Available in Google Classroom.

I Do

Multiple Choice

When f(x) = 9-3x and g(x) = 5x-7 , find f(x)+g(x). 

• 14x-10
• -8x+2
• 2x+2
• 2x-2

I DO

Multiple Select

Perform  $2\cdot f\left(x\right)\ +3\cdot g\left(x\right)$  given  $f\left(x\right)=4x-4$  and  $g\left(x\right)=3x-3$  .  

•  $17x-17$ 

•  $13x-17$  

•  $35x-35$  

•  $17x-5$  

WE DO

Multiple Choice

f(x) = 4x+8
g(x) = x+3,
Find f(x)*g(x)

• 4x²+24
• 4x²+20x+24
• 4x²+12x+24
• 4x²+4x+24

Can You Evaluate a Function?

Multiple Choice

If a question asks you to find f(2), what does that mean?

• Let x = 2

• Let y = 2

To Evaluate a Function ...

substitute the given value for x and simplify.

Multiple Choice

 $Given\ h\left(x\right)=x^2-4\ what\ is\ h\left(6\right)?$  

• 32

• 0

• -4

• 77

Multiple Choice

What is f(6) for the function f(x)=3x-8

• -8

• 10

• -144

• answer not here

How do you think we should do this next problem?

1. Substitute 2 for x in f(x) and 1 for x in g(x).

Then add the two values together.

Find g(3) - f(2)

Given the two functions...

Multiple Choice

g(x)=3x+4
h(x)=3x-1
Find g(h(x))

• -9x+11
• 4x²+4x
• 9x+1
• 9x+11

Multiple Choice

p(x) = 3x + 4
q(x) = 2x²
Find p(q(x))

• 10x²
• 18x² + 4
• 6x² + 4

Multiple Choice

f(x) = 3x + 10
g(x) = x - 2
Find f(g(5))

• 19
• 23
• -10
• None of these.