Remediation 1.1 CFA: Function Notation

VOCABULARY

Function Notation: a specific way to write a relation when it is a function. When you see a relation written in function notation you know right away that it is a function.

General Function Notation: f(x)

Said out loud: "f of x"

Example: y = 3x + 2 is a relation.

It is ALSO a function.

So it can be written as f(x) = 3x + 2

Multiple Choice

$$If\ h\left(x\right)\ =\ x^2-5x\ +\ 8\ ,\ \ \ Evaluate\ h\left(-6\right)$$  

• h(-6) = 2

• h(-6) = 36

• h(-6) = 74

• h(-6) = 14

Multiple Choice

Given g(x) = 4x - 7, find g(-9).

• g(-9) = 29

• g(-9) = -43

• g(-9) = 43

• g(-9) = -29

Math Response

Evaluate f(-4) if f(x) = 3x² - 4

Type answer here

Correct Answer: 44

Deg^°

Rad

Multiple Choice

What is x if
f(x) = -2?

• 4
• 0
• 3
• 8

Multiple Choice

Complete the function notation below
f(____) = 214

• 1990
• 1991
• 1989
• 1994

Multiple Choice

The graph shows the number of inches that it has been raining over 9 hours. After how many hours did it rain 4 inches?

• 2 hours

• 6 hours

• 3 hours

• 8 hours

Let's Practice evaluating tables!

Remember to ask yourself:

Am I given the input or the output? What am I asked to find?

Multiple Choice

Given the function table: what is t if h(t) = -5

• -1

• 1

• 0

• 2

Fill in the Blank

Using this table, find f(7).

Multiple Choice

Given the function table: determine h(-1)

• -8

• 1

• -5

• 2

Functions Operations: Add, Subtract, Multiply and Divide

Two or more function can be added, subtracted, multiplied or divided.

In the next slide are some examples of these using an f(x) and a g(x) function. The result is referred to as h(x).

Multiple Choice

Given
f(x) = 3x² + 7x and g(x) = 2x² - x - 1, find (f + g)(x).

• 11x² - 1
• 5x⁴ + 6x² - 1
• 5x² + 6x - 1
• 5x² + 8x - 1

Multiple Choice

f(x)=3x²+1
g(x)=4x+5
What is (f+g)(2)

• 13
• 0
• 26
• 6x²+8x+12

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

Fill in the Blank

Find $$(f-g)(2)$$ if $$f(x)=4x+10$$   and $$g(x)=3x-7$$  

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

Multiple Choice

Perform the indicated operation and evaluate at the given value.

Multiple Choice

f(x)= x+3

g(x)= x-2

Find (g(x) / f(x))

Be careful!!

• (x + 3)/(x - 2)

• (x - 2)/(x + 3)

• -2/3

• 3/2

Multiple Choice

What is (g/f)(-1)?

• -6
• -1
• 1/6
• 6

Multiple Choice

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

• $$4x^2-1$$  

• $$4x^2-2$$  

• $$8x^2-1$$  

• $$16x^2-1$$  

Multiple Choice

If $$f\left(x\right)=\frac{1}{x}$$   and  $$g\left(x\right)=3x+2$$   find $$\left(f\circ g\right)\left(2\right)$$  

• $$\frac{1}{4}$$  

• $$\frac{1}{8}$$  

• $$\frac{7}{2}$$  

• 8

Multiple Choice

If $$f\left(x\right)=2x$$   and  $$g\left(x\right)=2x^2-1$$   find $$f\left(g\left(3\right)\right)$$  

• 34

• 71

• 35

• 142

Multiple Choice

Given f and g in the graph,

what is (f ° g)(-1) ?

• 1

• 4

• -1

• 6

Multiple Choice

Given f and g in the graph,

what is f(g(2)) ?

• 3

• 8

• 1

• 4

Fill in the Blank

f(g(5)) =

-

Fill in the Blank

f(g(3)) =

Fill in the Blank

h(f(-2)) =

Fill in the Blank

f(f(0)) =