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Chapter 3 Review
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Gravity
Terms in this set (52)
How do you determine if a graph has origin symmetry?
f(-x) = -f(x)
How do you determine if a graph has x-axis symmetry?
Check and see if when you plug in (x,y) and (x,-y) if your equation stays the same.
How do you determine if a graph has y-axis symmetry?
Check and see if when you plug in (x,y) and (-x,y) if your equation stays the same.
How do you determine if a graph has symmetry with respect to the line y=x?
Plug in (x,y) and (y,x) and see if your equation stays the same.
How do you determine if a graph has symmetry with respect to the line y=-x?
Plug in (x,y) and (-y,-x) and see if your equation stays the same.
even functions are symmetric about the ______
y-axis
odd functions are symmetric about the __________
origin
I am the function y=x
...
I am the function: y=x^2
...
I am the function: y=x^3
...
I am the function: y=√x
...
I am the function: y=1/x
...
I am the parent function: y=|x|
...
Reflect across x-axis
y=-f(x)
Reflect across y-axis
y=f(-x)
How do you translate a parent function up?
y=f(x)+c
How do you translate a parent function down?
y=f(x)-c
How do you translate a parent function left?
y=f(x+c)
How do you translate a parent function right?
y=f(x-c)
What happens when you multiply any parent function by a fraction (does not matter if on the inside or outside of the parent function)?
It gets closer to the x-axis.
What happens when you multiply any parent function by a whole number (does not matter if on the inside or outside of the parent function)?
It gets closer to the y-axis
What is the scale factor, and what variable is it affecting when the dilation is being multiplied on the outside of the parent function (y= c*f(x))
Its just c, and you multiply c by y.
What is the scale factor, and what variable is it affecting when the dilation is being multiplied on the inside of the parent function (y= f(cx))
Its 1/c - you flip the fraction. You multiply the SF by x
When is an inequality a solid line?
≥ or ≤
When is an inequality a dashed line?
> or <
How do you know where to shade in an transformed inequality problem?
Test a point!
How do you find the inverse of a function?
1. Put in "y = " form,
2. switch x and y,
3. solve for y
How do you test to see if a function is continuous at a given point?
1. f(c) exhists (plug in the given points to the equation)
2. The function approaches the same value on the left and right of c
3. The y values that the function approaches from each side is f(c)
What is the end behavior when the degree is even?
Both ends point the same direction.
What is the end behavior when the degree is odd?
Both ends point opposite dierections.
What is the end behavior when the leading coefficient is positive?
Both ends either point up if the degree is even, or if the degree is odd, it starts in negative on the left and goes positive on the right (looks like a positive slope)
What is the end behavior when the leading coefficient is negative?
Both ends either point down if the degree is even, or if the degree is odd, it starts in positive on the left and goes negative on the right (looks like a negative slope)
How do you check to see if a given critical point is a max, min, or point of inflection?
Find f(the critical point) then find f(the critical point - 0.1) and f(the critical point + 0.1). Then check to see what those y values say about the left and right of the critical point.
When there is a maximum what is happening on the left and right of the function?
The y-values on the left and right of the critical point are both less than the y-value at the critical point.
When there is a minimum what is happening on the left and right of the function?
The y-values on the left and right of the critical point are both greater than the-y value at the critical point.
When there is a point of inflection what is happening on the left and right of the function?
One value will be greater than the y-value from the critical point and one y-value will be less than the y-value given at the critical point.
How do you find a vertical asymptote?
set denominator equal to zero
How do you find holes in a function?
Find the zeros of the top and bottom and see if any cancel out. The items that cancel out are the holes
How do you find horizontal asymptotes?
Check the degree of the numerator and denominator
What happens when the degree of the numerator is equal to the degree of the denominator?
then y=(leading coefficient of numerator)/(leading coefficient of denominator) is the horizontal asymptote
What happens when the degree of the numerator is less than the degree of the denominator?
y=0 is the horizontal asymptote
What happens when the degree of the numerator is greater than the degree of the denominator?
There is no horizontal asymptote
When is there a slant asymptote?
If the degree in the numerator is exactly one greater than the degree in the denominator
What process do we do to determine a slant asymptote?
Long Division
What is the formula for direct variation?
y = kx
What is the formula for inverse variation?
y=k/x
What is the formula for joint variation?
y=kxz
What is the formula for combined variation?
y=kx/z
What is the formula for this statement: y varies directly as x squared
y=kx^2
What is the formula for this problem: y varies jointly with x and z
y=kxz
What is the formula for this problem: P varies directly as V and inversely as R.
P=(kV)/(R)
What is the order for parent graph transformations?
1. Horizontal Translation
2. Dilations
3. Reflecting
4. Vertical Translation
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