Unit 1
f(x)= f(-x), both sides end in the same direction
What is.. even symmetry
The function f(x) = 2(0.6)^x shows exponential ______
What is exponential decay?
The smallest change in x-values it takes for the function to repeat itself
What is a period?
This is the simplified form of logb(xy)\log_b(xy)logb(xy).
What is logb(x)+logb(y)\log_b(x) + \log_b(y)logb(x)+logb(y)?
The side opposite the right angle
Holes occur in a rational function if...
there is a matching factor on the top and bottom
A function that models the scenario, 900 grams of radioactive material m decays at a rate of 2.6% per year t.
What is 900(97.4)^t?
The Amplitude, Max value, Min Value, and X-intercepts of the function y=-2sinx.
What is Ampltiude 2, Max 2, Min -2, x-intercepts 0, π, 2π -π , -2π?
Find the average rate of change of
k(x)=x^2 over the interval [-7,2]
.
What is -5?
Define a one-to-one function
No horizontal line intersects more than once. Each output value has a unique input value
The equation for Average Rate of Change
What is y2-y1/x2-x1
f(x)=x^2-4 and g(x)=3-x. f(g(5)) is this.
What is 0?
A sine function that has the following attributes: Amp 3, Period π, Phase Shift left 8, Vertical Shift down 4.
What is y=3sin(2(x+π/8))-4?
The graph of f(x)=2x+3−5f(x) = 2^{x+3} - 5f(x)=2x+3−5 is the result of these transformations applied to y=2xy = 2^xy=2x.
What is a shift left 3 units and down 5 units?
Cos(pi)
-1
The third term in the expansion of the function f(x)=(2x+3)^6
What is 2160x^4?
The inverse of the function g(x)=ln(2x+3)+10
What is e^x-13/2?
This is the maximum number of turning points the graph of f(x)=x5−2x3+1f(x) = x^5 - 2x^3 + 1f(x)=x5−2x3+1 can have.
What is 4?
A population of bacteria triples every hour. If there were 100 bacteria initially, this is the equation that models the population after ttt hours.
What is P(t)=100⋅3tP(t) = 100 \cdot 3^tP(t)=100⋅3t?
tan(pi/2)
what is Undefined
The term for a sequence with a common difference or constant rate of change
What is an Arithmetic Sequence?
The domain, range and asymptotes of the function f(x)=ln(4-x)+2
What is Asymptote:x=4, Domain:(-∞,4), Range:(-∞, ∞)?
This is the inverse of f(x)=2x+5
What is f^-1(x)= x-5/2
The solution to log2(x+1)=4\log_2(x + 1) = 4log2(x+1)=4.
What is x=15?
This type of function best models data that grows by equal factors over equal intervals.
What is an exponential function?