U2 A1- Exponents And Logs Flashcards
What are the restrictions on
y=ab^x
a can’t equal 0
b>0
b can’t equal 1
x is an element of the real numbers
Why can’t b=1 in y=ab^x
You get the same value regardless of what exponent it is (so you’d get a linear function)
Graph of decay functions: ___ from left to right
Fall
Graph of growth functions: ____ from left to right
Rise
What is the domain and range of an exponential function
Domain: (-infinite, infinite)
Range: (0,infinite)
What is the x intercept of an exponential function
None
What is the y intercept of an exponential function
(0,1)
What is the horizontal asymptote in exponential equations
y=0 (x axis)
Why is y=(1/2)^x a reflection about the y axis compared to
y=2^x
You can see that the base is flipped and in order to flip the base you have to make the exponent negative
Since x is now negative there’s a reflection about the y axis
In y=ab^x what determines whether the function rises or falls
b value
Exponential functions: b>1 means the function will ____
Rise
Exponential functions: 0<b></b>
Fall
Exponential functions: what does “a” represent
y intercept
What is the equation that represents an exponential function
y=ab^x
Exponential functions: as the value of b increases, the curve has a _____ rise
Steeper
Exponential functions: as the value of b decreases, the curve has a steeper ____
Fall
Exponential functions: when determining transformations do you still have to remember (x-h)
Yes
What is anything to the exponent 0
1
Exponential functions: a negative exponent causes the base to ____
Flip
What is the negative exponents law
(a/b)^-m = (b/a)^m
What is the power of a power law
(a^m)^n= a^m(n)
What is the rational exponents law
(n exponent root x)^m =
x^(m/n)
How can you solve an exponential equation graphically
y1= one side of the equation
y2= other side of the equation
point of intersection is the solution
Steps for solving exponential equations by changing the base
1) write both sides of the equation in the same base
2) use exponent laws so that each side of the equation only has 1 power
3) cancel out the bases
4) solve for x