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34 Cards in this Set

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Domain is
for x
Range is
for y
When is it a function of x?
When it passes the vertical line test.
When you evaluate things like f(2), f(-2), f(a), f(-a), f(a+1), for f(x) = 3x^2 -x +2 what do you do?
you plug whatever is in parenthasis for f(___) into the x part of the problem and then solve.
Evaluate
f(x)=4+3x-x^2

[f(3+h)-f(3)]/h
You solve each part seperately and plug it all in. So find f(3+h) and f(3) and then put it into the equation of
[f(3+h)-f(3)]/h
How do you find the domain?
You solve for the bottom to where it can't = 0.
What do you do when you find an expression?
With a graph give you make a piece-wise answer. Find the slope and then use y-y1=m(x-x1) to find the line. Circles = roots.
How to tell even, odd or neither?
You plug (-x) into the x's of the problem. Even = original. Odd = -(original). Neither is if you get something completely different.
Polynomial function
y = x^2 + x +1 with a degree of 2
Cubic function
y = x^3 - x +1
y = x^4 - 3x^2 + x
y = 3x^5 - 25x^3 + 60x
Power function
y = x^n
Root function
y = x^(1/n)
y = √x
Reciprocal function
y = x^-1
y = (1/x)
Rational function
y = (2x^4 - x^2 +1)/(x^2 - 4)
Algebraic function
y = √(x^2 +1)
Trigonometric functions
y = sinx
Exponential functions
y = 2^x
Logarithmic functions
y = log3X
Find least squares regression line
use Lin Reg (ax + b)
Shift the graph up
y= f(x) +c
shift down
y = f(x) - c
Shift right
y = f(x-c)
Shift left
y = f(x+c)
Reflect about the x axis
y = -f(x)
Reflect about the y axis
y = f(-x)
Stretch vertically
y = cf(x)
Compress vertically
y = (1/c)f(x)
f o g means
g(x) goes into f(x)
g o f means
f(x) goes into g(x)
When you have a graph with two graphs on it, what does f(g(2)) mean?
You find g(2) and then the answer to that means f(answer).
What does "Find all solutions of the equation correct to two decimal places" mean?
You have to find to two equations by setting them equal to each other.
X^3-9X^2-4=0 ==> x^3=9X^2+4
Then find the intersection in the calculator.
What do you do when you have a graph and f(x)=Ca^x?
You plug the points into x & y from the equation. Then you divide them byeach other to get rid of C. Take the root of the a to find the answer.
logax=y
a^y=x
Evaluate log 8(5)
ln5/ln8 = .773976