Function Family Album

Exponential Functions Transformation Information:

Exponential Functions Information For A Parent Function:

Asymptote: 0

X-intercept: None (N/A)

Y-intercept: 1

Maximum: Infininty, approaching infinity

Minimum: 0, but it never actually touches 0

Vertex: None (N/A) unless two intersect

Function: y = 2^x

Vertical shift ex: y = 2^x + 3

Horizontal shift ex: y = 2^(x-1)

Vertical stretch ex: y = (2)2^x

Final Equation: y = (2)2^(x-1) +3

Real World Pic as clipart - macaroni noodles have a bent and exponential shape

Exponential Function Table & Graph

Equation: f(x) = 2^x

Exponential Function

Parent Function: y=b^x (where b is a positive non zero number)

Standard Form: f(x) = a^x + b -

If A is a decimal or fraction then the line will decrease quickly approaching zero. If A is an integer, than it will approach infinity. The bigger the value of X than the bigger the exponential growth. The smaller the value of X than the greater the exponential decay (approaching zero)

Domain of parent function: (∞, ∞)

Range of parent function: (0, ∞)

Function Family Album

Linear Function!

Linear Function Facts:

-Parent Function: y = x

-Standard Form: y = mx + b

-B is the y-intercept

-M is the slope

Real World Pic - The bat is a linear line at a 90 degree angle

By: Sophia Deshmukh

The following data is as followed from the equation y = 2x+3:

- X Intercept =-1.5

- Y Intercept = 3

- Vertex = none (N/A)

- Asymptote = none (N/A)

- Max/min value = none (N/A)

Linear functions always are a straight line that run forever, and have no beginning or ending because the plug in values are limitless.

Linear Function Equation Table

Value Table

EXAMPLE:

Equation: y = 2x + 3

Inverse of Equation: y = x-3/2

Linear Functions Transformations

Transformations of Linear Function Graph:

Taken from the function y = f(x), the transformations are as follows:

• y = 2x + 3 + 4 [vertical shift of up 4]
• y = 2(x-1) + 7 [horizontal shift of right 1, up 4 vertically]
• y = 1/2(2)(x-1) + 7 [vertical stretch of 1 now, vertical shift of up 4, horizontal shift of right 1]

Domain and Range of y = 1(x-1) + 7

Domain: All real numbers

Range: All real numbers

Symmetric about the y-axis

Symmetric about the x-axis