pre calc

difference of squares formula

a2-b2 = (a+b)(a+b)

sum of cubes formula

a3+b3 = (a+b)(a2-ab+b2)

difference of cubes formula

a3-b3 = (a-b)(a2+ab+b2)

when a function has no square root or fraction the domain is…

all reall numbers

when a function has a square root the domain is

the equation under the square root, greater or equal to 0

when the function is a fraction the domain…

the x in the denominator cannot make the equation 0

what is the formula for average rate of change?

f(b)-f(a)/b-a

domain is…

left to right

range is…

down and up

x-intercepts is…

where the line crosses the x intercept at a point

positive intervals is…

where the graph is above the x-axis, y>0, hilltops

negative intervals is…

where the graph is below the x-axis, y<0, valleys

relative extrema

peaks or valleys on the graph

absolute extrema

the highest or lowest point on the entire graph

increasing intervals

where the line goes uphill moving left to right, is y getting bigger?

decreasing intervals

where the line goes downhill moving left to right, is y getting smaller?

constant intervals

where the graph is flat in a horizontal line

even/odd/neither

symmetry where even mirrors over y-axis, odd is rotated 180 or neither

end behavior

where the arrows go, as x gets bigger or tinier, where does the line head to?

where should you look for intervals?

x-axis

y=x OR y=mx+b

y=x^2

y=|x|

y=x^3

y=sqaure root of x

y= ^3 square root of x

y=1/x

y=2x

y=log2(x)