EDG 2.1-3 Remediation

EDG 2.1-3 Remediation

Complete this lesson and take the Quizizz to improve your formative Quiz 2.1-3 grade.

FUNCTION OPERATIONS

To add, just combine like terms

Multiple Choice

f(x) = 9-3x
g(x) = 5x-7
Find f(x)+g(x). 

• 14x-10
• -8x+2
• 2x+2
• 2x-2

Remember to distribute the negative when subtracting

Multiple Choice

f(x) = x²+9
g(x) = x-9
Find f(x)-g(x). 

• x²+x+9
• x²-x+9
• x²-x
• x²-x+18

sometimes you have to distribute or FOIL when you multiply functions

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

Evaluating Functions

to 'evaluate' means to plug in and get a number answer

Sometimes, you have to do an operation AND evaluate.

In this example, we add the functions, and plug a 5 into each one. The answer is 38.

Multiple Choice

Evaluate f(x) = -5x + 8 at f(3)

• -7
• 7
• 0

Multiple Choice

Perform the indicated operation and evaluate at the given value.

Multiple Choice

Perform the indicated operation and evaluate for the given value.

Multiple Choice

Complete the operation and evaluate.

COMPOSITION

(plugging one function into another)

Study the example to the right--->

There are 2 notations for composition.

Multiple Choice

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

• 3x² - 2
• 3x + 8
• 3x + 4
• None of these.

Multiple Choice

f(g(x))

• 3x - 16

• 3x - 2

• 3x - 26

• 4x - 2

a hint for the next problem: You will have to FOIL. Then, distribute the 2

(Please Excuse My Dear Aunt Sally!)

Multiple Choice

p(x) = 3x + 4
q(x) = 2x²
Find q(p(x))

• 6x² + 4
• 18x² + 48x + 32
• 18x² + 32
• None of these.

Composition with Evaluating

notice how the 5 goes into function 'g' first. Then, that answer goes into function 'f'.

Multiple Choice

f(x) = 3x + 10
g(x) = x - 2
Find f(g(0))

• 16
• 4
• -4
• None of these.

Multiple Choice

Find f[g(5)]

• 30

• 242

• 92

• 2

Evaluating from a table

f(g(2)) = ?

Do g(2) first. The answer is 5. Then, do f(5). The answer is 6. Do you see???

Multiple Choice

• 3

• 1

• 4

• None of the Above

Evaluating from a graph

f(g(2)) = ???

Where is the output of g when x = 2? It's 1. Do you see the point (2,1)? Then, find f(1). It's -4

So, f(g(2)) = -4

Multiple Choice

Given f and g in the graph,
what is  $\left(f\circ g\right)\left(-1\right)?$ 

• 1

• 4

• -1

• 6

Multiple Choice

Given f and g in the graph,

what is f(g(2)) ?

• 3

• 8

• 1

• 4

INVERSES

Swap x and y

Solve for y

Write in inverse notation

EXTRA INVERSE NOTES:

• SWAP X AND Y TO FIND INVERSE FUNCTION POINTS

• REFLECT A GRAPH OVER Y=X TO FIND ITS INVERSE

• IF F(X) AND G(X) ARE INVERSES OF EACH OTHER... F(G(X)) = X AND G(F(X)) = X

Multiple Choice

What is the inverse of the given coordinates: (1, 2) (3, 8) (-3, 6)

• (1, 2) (3, 8) (-3, 6)
• (1, 2) (8, 3) (-3, 6)
• (-1, -2) (-3, -8) (3, -6)
• (2, 1) (8, 3) (6, -3)

Multiple Choice

The inverse has been reflected over which line?

• y = x
• y =1
• y = 0
• y = x + 1

Multiple Choice

The composition of any function, f(x), and
its inverse, f^-1(x) = 

• x
• f(x)
• 1
• 0

Multiple Choice

Find the inverse of
f(x) = 1/4x - 7

• f^-1(x) = 4x + 7
• f^-1(x) = -4x + 28
• f^-1(x) = -4x - 7
• f^-1(x) = 4x + 28

Multiple Choice

If the equation of f(x) goes through (1, 4) and (4, 6), what points does f^-1(x) go through?

• (1, 4) and (4, 6)
• (-4, -1) and (-6, -4)
• (-1, -4) and (-4, -6)
• (4, 1) and (6, 4)

Multiple Choice

Are the blue and red graphs inverse functions?

• yes
• no
• no way to tell

Multiple Choice

Are these inverse functions?

• no
• yes
• no way to tell

Multiple Choice

Are these functions inverses?

• Yes
• No

DOMAIN RESTRICTIONS

• WHAT X VALUES ARE NOT ALLOWED?

• THE DENOMINATOR CANNOT = 0 , SO SET THE DENOMINATOR = 0 AND SOLVE TO FIND WHAT X CANNOT BE

• WHAT IS INSIDE A RADICAL CANNOT BE NEGATIVE. SO, SET WHAT IS UNDER THE RADICAL  $\ge$   0, AND SOLVE. 

Multiple Choice

 $\frac{x-3}{\sqrt{x+2}}$  Choose the domain for which the function is defined.

•  $x\ge2$  

•  $x\ge-2$  

•  $x\le2$  

•  $x\le-2$  

Multiple Choice

 $\frac{3}{x+4}$  What is the restricted domain?

•  $x\ge4$  

•  $x\ge3$  

•  $x\ne3$  

•  $x\ne-4$