warm–up #3. warm–up #3 solutions homework log tues 11/3 lesson 3 – 2 learning objective: to...

Warm–up #31. Find domain & range

2. g(x) = , find g(x + h)

Warm–up #3 Solutions1. Find domain & range Domain: Range: [0, )2. g(x) = , find g(x + h)=

=

Homework LogTues

11/3

Lesson 3 – 2

Learning Objective: To find difference quotients & to graph functions

Hw: #304 Pg. 179 #45 – 51 odd, 54, 56, 57 – 63 odd, 64, 70 – 76 even

11/3/15 Lesson 3 – 2 Difference Quotients & Function Graphs Day 2

Advanced Math/Trig

Learning Objective

To find difference quotient

To evaluate functions

To graph absolute value and quadratic functions

To graph step functions

Difference QuotientUsed in Calculus to study tangent lines to curves

Find the Difference Quotient

1.

=

=

=

= =

Find the Difference Quotient

2. f(x) = 4x – 5

=

=

=

Find the Difference Quotient

3.

=

=

Find the Difference Quotient

3.

=

=

=

=

Function4. Determine if this is a function

No! It doesn’t pass the vertical line test.

Function GraphsAbsolute Value FunctionsVertex (h, k)

Quadratic Functions

To find the x value of the vertexx =

Plug back into original function to find y

5.

Vertex: (0, –4)

x y

V(0 – 4)

– 2– 1

1 2

– 2 – 3

– 3 – 2

Is a function.

Passes the vertical line test.

6. Vertex: (3, 0)

x y

V(3 0)

1 2

4 5

2 1

1 2

Is a function.

Passes the vertical line test.

7. Vertex: (–2, 3)

x y

V(– 2 3)

– 4 – 3

– 1 0

5 4

4 5

Is a function.

Passes the vertical line test.

8. Vertex: (0, 1)

x y

V(0 1)

– 2 – 1

1 2

5 2

2 5

x = = 0

y =

Is a function.

Passes the vertical line test.

9.

Vertex: (1, –5)

x y

V( 1 –5)

– 1 0

2 3

3 –3

–3 3

x = = 1

y =

Is a function.

Passes the vertical line test.

Greatest Integer Function

Greatest Integer x

1.

2.

3.

4.

5.

6.

7.

8.

–4 –3 –2 –1 0 1 2 3 4 5 6 7

= 5

= 0

Graph 9. Plug in positive decimal values 1 to get a pattern and then fill in the negatives.

1.01.21.92.02.22.93.0

x y

1112223

y

x

Is a function, so must pass the vertical line test.

Greatest Integer Function

9.

y

x

0 1x 1 2x 2 3x

1 0x 012

1

Actual Table: x y

y

x

Graph 10.

1.01.21.92.02.22.93.0

x y

3334445

y

x

Graph 11.

1.01.21.92.02.22.93.0

x y

–2–2–2–1–1–10

Evaluate 12.

Find f (1.3)

Plug into calculator!

= – 4.283

Evaluate the difference quotient

13. x = 4 and h = 0.02

=

Plug into calculator!

= 1.02

Ticket Out the Door

Find the difference quotient

f(x) =

Homework

#304 Pg. 179 #45 – 51 odd, 54, 56, 57 – 63 odd, 64, 70 – 76 even