+ All Categories
Home > Documents > Introduction So far we have seen a function f of a variable x represented by f(x). We have graphed...

Introduction So far we have seen a function f of a variable x represented by f(x). We have graphed...

Date post: 01-Jan-2016
Category:

Documents
Upload: damon-washington
View: 213 times
Download: 0 times
Download Report this document
Share this document with a friend
Popular Tags:
function fx
function notation43
f of x
variable x
f times x
range of fx
graphed fx
continuedevaluate f2
17
Introduction So far we have seen a function f of a variable x represented by f(x). We have graphed f(x) and learned that its range is dependent on its domain. But, can a function be applied to expressions other than x? What would it mean if we wrote f(2x) or f(x + 1)? In this lesson, we will explore function notation and the versatility of functions. 1 3.1.4: Function Notation and Evaluating Functions
Transcript
Page 1: Introduction So far we have seen a function f of a variable x represented by f(x). We have graphed f(x) and learned that its range is dependent on its.

IntroductionSo far we have seen a function f of a variable x represented by f(x). We have graphed f(x) and learned that its range is dependent on its domain. But, can a function be applied to expressions other than x? What would it mean if we wrote f(2x) or f(x + 1)? In this lesson, we will explore function notation and the versatility of functions.

1

3.1.4: Function Notation and Evaluating Functions

Page 2: Introduction So far we have seen a function f of a variable x represented by f(x). We have graphed f(x) and learned that its range is dependent on its.

Introduction, continuedFor example, let f be a function with the domain {1, 2, 3} and let f(x) = 2x. To evaluate f over the domain {1, 2, 3}, we would write the following equations by substituting each value in the domain for x:

f(1) = 2(1) = 2

f(2) = 2(2) = 4

f(3) = 2(3) = 6

{2, 4, 6} is the range of f(x).

2

3.1.4: Function Notation and Evaluating Functions

Page 3: Introduction So far we have seen a function f of a variable x represented by f(x). We have graphed f(x) and learned that its range is dependent on its.

Key Concepts• Functions can be evaluated at values and variables.

• To evaluate a function, substitute the values for the domain for all occurrences of x.

• To evaluate f(2) in f(x) = x + 1, replace all x’s with 2 and simplify: f(2) = (2) + 1 = 3. This means that f(2) = 3.

• (x, (f(x)) is an ordered pair of a function and a point on the graph of the function.

3

3.1.4: Function Notation and Evaluating Functions

Page 4: Introduction So far we have seen a function f of a variable x represented by f(x). We have graphed f(x) and learned that its range is dependent on its.

Common Errors/Misconceptions• thinking function notation means “f times x” instead of

“f of x”

• trying to multiply the left side of the function notation

4

3.1.4: Function Notation and Evaluating Functions

Page 5: Introduction So far we have seen a function f of a variable x represented by f(x). We have graphed f(x) and learned that its range is dependent on its.

Guided Practice

Example 1Evaluate f(x) = 4x – 7 over the domain {1, 2, 3, 4}. What is the range?

5

3.1.4: Function Notation and Evaluating Functions

Page 6: Introduction So far we have seen a function f of a variable x represented by f(x). We have graphed f(x) and learned that its range is dependent on its.

Guided Practice: Example 1, continued

1. To evaluate f(x) = 4x – 7 over the domain {1, 2, 3, 4}, substitute the values from the domain into f(x) = 4x – 7.

6

3.1.4: Function Notation and Evaluating Functions

Page 7: Introduction So far we have seen a function f of a variable x represented by f(x). We have graphed f(x) and learned that its range is dependent on its.

Guided Practice: Example 1, continued

2. Evaluate f(1).

7

3.1.4: Function Notation and Evaluating Functions

f(x) = 4x – 7 Original function

f(1) = 4(1) – 7 Substitute 1 for x.

f(1) = 4 – 7 = –3 Simplify.

Page 8: Introduction So far we have seen a function f of a variable x represented by f(x). We have graphed f(x) and learned that its range is dependent on its.

Guided Practice: Example 1, continued

3. Evaluate f(2).

8

3.1.4: Function Notation and Evaluating Functions

f(x) = 4x – 7 Original function

f(2) = 4(2) – 7 Substitute 2 for x.

f(2) = 8 – 7 = 1 Simplify.

Page 9: Introduction So far we have seen a function f of a variable x represented by f(x). We have graphed f(x) and learned that its range is dependent on its.

Guided Practice: Example 1, continued

4. Evaluate f(3).

9

3.1.4: Function Notation and Evaluating Functions

f(x) = 4x – 7 Original function

f(3) = 4(3) – 7 Substitute 3 for x.

f(3) = 12 – 7 = 5 Simplify.

Page 10: Introduction So far we have seen a function f of a variable x represented by f(x). We have graphed f(x) and learned that its range is dependent on its.

Guided Practice: Example 1, continued

5. Evaluate f(4).

10

3.1.4: Function Notation and Evaluating Functions

f(x) = 4x – 7 Original function

f(4) = 4(4) – 7 Substitute 4 for x.

f(4) = 16 – 7 = 9 Simplify.

Page 11: Introduction So far we have seen a function f of a variable x represented by f(x). We have graphed f(x) and learned that its range is dependent on its.

Guided Practice: Example 1, continued

6. Collect the set of outputs from the inputs.

The range is {–3, 1, 5, 9}.

11

3.1.4: Function Notation and Evaluating Functions

✔

Page 12: Introduction So far we have seen a function f of a variable x represented by f(x). We have graphed f(x) and learned that its range is dependent on its.

12

3.1.4: Function Notation and Evaluating Functions

Guided Practice: Example 1, continued

12

http://walch.com/ei/CAU3L1S4EvalFunc1
Page 13: Introduction So far we have seen a function f of a variable x represented by f(x). We have graphed f(x) and learned that its range is dependent on its.

Guided Practice

Example 3Raven started an online petition calling for more vegan options in the school cafeteria. So far, the number of signatures has doubled every day. She started with 32 signatures on the first day. Raven’s petition can be modeled by the function f(x) = 32(2)x. Evaluate f(3) and interpret the results in terms of the petition.

13

3.1.4: Function Notation and Evaluating Functions

Page 14: Introduction So far we have seen a function f of a variable x represented by f(x). We have graphed f(x) and learned that its range is dependent on its.

Guided Practice: Example 3, continued

1. Evaluate the function.

14

3.1.4: Function Notation and Evaluating Functions

f(x) = 32(2)x Original function

f(3) = 32(2)3 Substitute 3 for x.

f(3) = 32(8) Simplify as needed.

f(3) = 256

Page 15: Introduction So far we have seen a function f of a variable x represented by f(x). We have graphed f(x) and learned that its range is dependent on its.

Guided Practice: Example 3, continued

2. Interpret the results. On day 3, the petition has 256 signatures. This is a point on the graph, (3, 256), of the function f(x) = 32(2)x.

15

3.1.4: Function Notation and Evaluating Functions

Page 16: Introduction So far we have seen a function f of a variable x represented by f(x). We have graphed f(x) and learned that its range is dependent on its.

Guided Practice: Example 3, continued

16

3.1.4: Function Notation and Evaluating Functions

✔

Nu

mb

er o

f si

gn

atu

res

Days

Page 17: Introduction So far we have seen a function f of a variable x represented by f(x). We have graphed f(x) and learned that its range is dependent on its.

17

3.1.4: Function Notation and Evaluating Functions

Guided Practice: Example 3, continued

17

http://walch.com/ei/CAU3L1S4EvalFunc2

Recommended
STAT509 Continuous Probability Distributions Recall: P(a < X < b) = = F(b) – F(a) F (a) = μ = E[X] = 2 = E[X 2 ] – μ 2 f(x) x x F(x)

STAT509 Continuous Probability Distributions Recall: P(a < X < b) = = F(b) – F(a) F (a) = μ = E[X] = 2 = E[X 2 ] – μ 2 f(x) x x F(x)

Documents

Cadenas de Markov y Teoría de Colas - materias.fi.uba.armaterias.fi.uba.ar/6615/Material/markov.pdf · n m m k k m n m k n k m f x x f x x f x f x x f x x f x f x f x x x f x x x

Cadenas de Markov y Teoría de Colas - materias.fi.uba.armaterias.fi.uba.ar/6615/Material/markov.pdf · n m m k k m n m k n k m f x x f x x f x f x x f x x f x f x f x x x f x x x

Documents

Topic 10: Integration - Trinity College Dublin · 2019. 1. 3. · 3 Definition Just as f(x) = derivative of F(x) F(x) =∫f (x)dx Example F ( x ) = ∫3 x 2 dx = x 3 + c c=constant

Topic 10: Integration - Trinity College Dublin · 2019. 1. 3. · 3 Definition Just as f(x) = derivative of F(x) F(x) =∫f (x)dx Example F ( x ) = ∫3 x 2 dx = x 3 + c c=constant

Documents

NAME DATE PERIOD 9 Chapter 9 Test, Form 2B · NAME DATE PERIOD 9 Chapter 9 Test, Form 2B (continued) 11. Which rational function is graphed? A f(x) = !!!!! Cf(x) = D f(x) = ! 2 B

NAME DATE PERIOD 9 Chapter 9 Test, Form 2B · NAME DATE PERIOD 9 Chapter 9 Test, Form 2B (continued) 11. Which rational function is graphed? A f(x) = !!!!! Cf(x) = D f(x) = ! 2 B

Documents

M3309-F10Week 11.2 FG x + F(x)F(x) G(x)G(x) F(x) + G(x)

M3309-F10Week 11.2 FG x + F(x)F(x) G(x)G(x) F(x) + G(x)

Documents

Practice Problems for Test 1 · Practice Problems for Test 1 Page 3 of 12 8. 9. ID: 2.3.59 For the function graphed to the right, explain why lim f(x)≠3. x→4 0 2 4 6 8 0 2 4 6

Practice Problems for Test 1 · Practice Problems for Test 1 Page 3 of 12 8. 9. ID: 2.3.59 For the function graphed to the right, explain why lim f(x)≠3. x→4 0 2 4 6 8 0 2 4 6

Documents

x) · cot x = ¯csc 2 x d dx sec x = sec x tan x f(t) = 1 2 gt 2 + v 0 t + s0 v(t) = f'(t) a(t) = v'(t) = f"(t) d dx csc x = ¯csc x cot x d dx (f(x)⋅g(x))= f(x)g'(x)+ g(x)f'(x)

x) · cot x = ¯csc 2 x d dx sec x = sec x tan x f(t) = 1 2 gt 2 + v 0 t + s0 v(t) = f'(t) a(t) = v'(t) = f"(t) d dx csc x = ¯csc x cot x d dx (f(x)⋅g(x))= f(x)g'(x)+ g(x)f'(x)

Documents

Graphed Grant Results

Graphed Grant Results

Education

Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

Derivatives of Trig Functions Intro 081 - Chipola College · 2017-07-13 · Derivatives of Trig Functions IF: THEN: F(x) = sin x F'(x) = cos x F(x) = cos x F'(x) = - sin x F(x) =

Documents

Let f I x y in the interval I f x

Let f I x y in the interval I f x

Documents

This time (f+g)(x)=f(x)+g(x) (f-g)(x)=f(x)-g(x) (fg)(x)=f(x)*g(x) (f/g)(x)=f(x)/g(x), g(x)≠0 (f ∘ g)(x)=f(g(x))

This time (f+g)(x)=f(x)+g(x) (f-g)(x)=f(x)-g(x) (fg)(x)=f(x)*g(x) (f/g)(x)=f(x)/g(x), g(x)≠0 (f ∘ g)(x)=f(g(x))

Documents

1-6 Function Operations and Composition of · PDF fileFind ( f + g)(x), (f ± g)(x), (f { g)(x), and (x) for each f(x) and g(x). State the domain of each new function. f(x) = x2 +

1-6 Function Operations and Composition of · PDF fileFind ( f + g)(x), (f ± g)(x), (f { g)(x), and (x) for each f(x) and g(x). State the domain of each new function. f(x) = x2 +

Documents

Integral ch 7 - ncert.nic.inncert.nic.in/textbook/pdf/lemh201.pdf · ∫f x dx() Integral of f with respect to x f(x) in ∫f x dx() Integrand x in ∫f x dx() Variable of integration

Integral ch 7 - ncert.nic.inncert.nic.in/textbook/pdf/lemh201.pdf · ∫f x dx() Integral of f with respect to x f(x) in ∫f x dx() Integrand x in ∫f x dx() Variable of integration

Documents

Edl...7) If the function f (x) — — 3 is translated 2 units down, and 5 units to the left, find the graph that matches the new function: new % S I l) Mr. Livingston graphed the

Edl...7) If the function f (x) — — 3 is translated 2 units down, and 5 units to the left, find the graph that matches the new function: new % S I l) Mr. Livingston graphed the

Documents

Chemistry Project Work Mavis Lau F.3A (16). Name: Nitrogen Trifluoride Formula: NF3 Electron diagram: N F F F O O O O O X X XX XX X X X X XX X X XX X.

Chemistry Project Work Mavis Lau F.3A (16). Name: Nitrogen Trifluoride Formula: NF3 Electron diagram: N F F F O O O O O X X XX XX X X X X XX X X XX X.

Documents

DERIVATIVES 3. Summary f(x) ≈ f(a) + f’(a)(x – a) L(x) = f(a) + f’(a)(x – a) ∆y = f(x + ∆x) – f(x) dx = ∆x dy = f’(x)dx ∆ y≈ dy.

DERIVATIVES 3. Summary f(x) ≈ f(a) + f’(a)(x – a) L(x) = f(a) + f’(a)(x – a) ∆y = f(x + ∆x) – f(x) dx = ∆x dy = f’(x)dx ∆ y≈ dy.

Documents

funcy Documentation · string re_finder(f) re_tester(f) int or slice itemgetter(f) itemgetter(f) mapping lambda x: f[x] lambda x: f[x] set lambda x: x in f lambda x: x in f 2.1Supporting

funcy Documentation · string re_finder(f) re_tester(f) int or slice itemgetter(f) itemgetter(f) mapping lambda x: f[x] lambda x: f[x] set lambda x: x in f lambda x: x in f 2.1Supporting

Documents

ECONOMICS 1. f X S Y f Y f M X

ECONOMICS 1. f X S Y f Y f M X

Documents