Exponent Laws
For bx, b is referred to as the __________, and x is referred to as the _______.
For bx, b is referred to as the BASE and x is referred to as the POWER or EXPONENT
What are the 3 methods we have learnt to solve exponential equations?
1. Estimate and Check (or guess and check)
2. Common Bases
3. Graphing
Exponential Functions are often referred to as "________" functions because of their unique shape
Hockey Stick
How does the 'c' parameter transform an exponential function?
This moves the graph up or down along the y-axis. If c is positive the graph will be translated up c units, if c is negative the graph will be translated down c units.
The original value of a function is denoted with what variable. What does "original value" mean?
Variable a or f0. This is the starting value or the value when x = 0
What is the name of the following exponent law:
bx X by = bx+y
Product Rule.
True or false: You can use any method we have learnt to solve any exponential equation.
Explain your reasoning.
FALSE: You may not be able to use common bases if you cannot re-write both sides of the equation to have the same base
True or false: the Domain for all exponential functions will be the same?
If true state what the domain is, if false explain why it is not the same.
TRUE. x is an element of the real numbers.
How does the 'd' parameter transform an exponential function?
This moves the graph left or right along the x-axis. If written in the form (x - d) the graph will be translated right d units, if written in the form (x + d) the graph will be translated left d units.
For functions with the form f(x)= abx, the growth or decay factor is represent by the variable ____ is is growing when ________ and decaying when __________
b
b is greater than 1
b is in between zero and 1
Complete the following exponent law:
(ab)x = ___________.
axbx
Solve for x: 42x+2 = 43x
x= 2
For all exponential functions in the form bx , there will be a horizontal asymptote at _____________.
y = 0
How does the 'a' parameter transform an exponential function?
This parameter will vertically stretch or compress an exponential function.
For functions with the form f(x)= abx what does x represent?
x represents how often the growth or decay occurs.
Simplify: (16x3y-5)/ (4x-6y8)
(4x9) /(y13)
Solve for x: (3(-3x))(3x) = 27
x = -3/2
What are the three anchor points of the functions bx
1) horizontal asymptote at y = 0
2) pass through the point (0,1)
3) pass through the point (1, b)
How does the 'k' parameter transform an exponential function?
This parameter will horizontally stretch or compress an exponential function.
A new car cost $24,000 and it loses 18% of its value each year after it is purchased. Write an equation that models this.
f(t) = 24,000(0.82)t
Simplify: ((36x2y3)1/2) / (61/2)2
6xy3/2
Solve for x: 22x +3 = 1
x = -3/2
State all the properties of the function: F(x) = -6x
Domain: x is an element of the real numbers
Range: y is an element of the real numbers such that y is smaller than zero
Horizontal Asymptote: y = 0
Interval: Decreasing
Intercepts: No x intercept, y-intercept at (0,-1)
State all the properties of the following function:
f(x) = 2-(x+2) - 2
Domain: x is an element of the real numbers
Range: y is an element of the real numbers such that y is greater than -2
Horizontal asymptote: y =-2
Interval: Decreasing
y-intercept: (0,-1.75)
x-intercept (-3, 0)
A new car cost $24,000 and it loses 18% of its value each year after it is purchased. Determine the value of the car after 30 months rounded to 2 decimal points