Calculus Final Review Common Functions Flashcards
y=x^2
An upward “u”
y=x^2
An upward “u”
x=y^2
A sideways “u”
x=y^2
A sideways “u”
y=x^3
1/2(downward “u”), then 1/2 ( upward “u”)
y=x^3
1/2(downward “u”), then 1/2 ( upward “u”)
y=x^1/3
Previous; sideways and rotated
y=x^1/3
Previous; sideways and rotated
y=x
Straight diagonal line
y=x
Straight diagonal line
y=1/x
Opposing curves against “x” and “Y”
y=1/x
Opposing curves against “x” and “Y”
y=1/x^2
From x backwards up to y
y=1/x^2
From x backwards up to y
y=[x]
Upward “v”
y=[x]
Upward “v”
y=[x]/x
Open circles, then constant y=some # x
y=[x]/x
Open circles, then constant y=some # x
y=(a^2-x^2)^1/2
Semicircle
y=(a^2-x^2)^1/2
Semicircle
y=-f(x)
Reflects the graph over the x-axis
y=-f(x)
Reflects the graph over the x-axis
y=f(-x)
Reflects the graph over the y-axis
y=f(-x)
Reflects the graph over the y-axis
y=f(x)+c
Translates the graph of y=f(x) up c units
y=f(x)+c
Translates the graph of y=f(x) up c units
y=f(x)-c
Translates the graph of y=f(x) down c units
y=f(x)-c
Translates the graph of y=f(x) down c units
y=f(x+c)
Translates the graph of y=f(x) left c units
y=f(x+c)
Translates the graph of y=f(x) left c units
y=f(x-c)
Translates the graph of y=f(x) right c units
y=f(x-c)
Translates the graph of y=f(x) right c units
y=cf(x)
The graph of y=f(x) scaled vertically by c (c>0)
y=cf(x)
The graph of y=f(x) scaled vertically by c (c>0)
A plane curve is symmetric about the —if replacing — by —- in its equation produces and equivalent equation.
y-axis, x, -x,
A plane curve is symmetric about the —if replacing — by —- in its equation produces and equivalent equation.
y-axis, x, -x,
A plane curve is symmetric about ——- if replacing —- by —- and —- by —- in its equation produces and equivalent equation.
the origin, x, -x, y, -y
A plane curve is symmetric about ——- if replacing —- by —- and —- by —- in its equation produces and equivalent equation.
the origin, x, -x, y, -y
m=(y_2-y_1)/(x_2-x_1)
Slope
m=(y_2-y_1)/(x_2-x_1)
Slope
y-y_1=m(x-x_1)
Point-slope form
y-y_1=m(x-x_1)
Point-slope form
