Bellwork1) Do a Grade check (note both your quarter grade and semester grade)2) Pull out your parent function booklet.3) Take a minute to tidy up your binders!

Parent Function: Exponential

Let’s add this to your parent Function Booklet!

x -1 0 1 2 3

y

(1, 2)(0, 1)(-1, ½) (2, 4) (3, 8)

Graph Exponential Functions- Using a table

x y

-4

-3

-2

-1

0

-6

-5

-4.5

-4.25

-4.125

Asymptote- A line that a curve gets infinitely close to, but never touches

x y

-4

-3

-2

-1

0

-6

-5

-4.5

-4.25

-4.125

y=-4

Transformations- -Exponential Functions

a vertically stretches or shrinks the graph of y = bx .

If there is not a number where a is, it is either 1 or -1

Transformations- -Exponential Functions

.b is always the number actually touching the exponent. b is never negative or 0

Transformations- -Exponential Functions

h translates (moves) the graph horizontally.

h is always the number that is part of the exponent, and is always opposite of its appearance. If there’s not a number there, h is 0.

Transformations- -Exponential Functions

k translates (moves) the graph vertically.

k is always the number added at the end of the equation. If there’s not a number there, k is 0. Because the value of k shifts the entire graph vertically, the graph’s asymptote is always y = k.

Increasing/Decreasing

The sign of a (+ or –) and the size of b (b > 1 or 0 < b < 1) determine where and if the graph is increasing or decreasing. The following chart defines this:

Identify a, b, h, and k

Finding points

You can use these formulas for finding two specific points in every exponential equation using the values of a, b, h, and k.

(h, a + k) and (h + 1, ab + k).

These formulas usually lead to nice ‘plottable’ (often whole) numbers.

SAMPLE PROBLEM:

Compare the exponential equation to the generic form and identify a, b, h, and k:  y = abx – h + k

y = 2x – 2 + 3 

Step 1:

a = 1 b = 2 h = 2 k = 3Since there’s not a numberbefore the ‘b’

Since it was -2, it’s +2

 Substitute into the point formulas, point #1 is (h, a+k)

 point #2 is (h+1, ab+k)

SAMPLE PROBLEM:

Step 2:

a = 1, b = 2, h = 2, and k = 3.

(2, 1+3) or (2, 4)

(2+1, 1(2)+3) or (3,5)

a = 1, b = 2, h = 2, and k = 3.Step 3:

SAMPLE PROBLEM:

Graph:

1) Draw and label the

asymptote (dotted line “barrier”)

2) Plot and label the two points

3) Neatly draw the smooth exponential curve through the two points, making sure it approaches, but never touches, the asymptote

4) Label the curve.

Step 3:

Let’s look at the assignment…