function families & key features toolkit - math

y-intercept

where a curve crosses/touches the y axis (where x=0)

x-intercept(s)

where a curve crosses/touches the x-axis (where y=0)

maximum

the highest point on a curve

minimum

the lowest point on a curve

decreasing

when y-values decrease as x-values increase

increasing

when y-values increase as x-values increase

asymptote

lines that the curve approaches (gets close to but never reaches)

linear equation

y=x

exponential equation

y=b^x

quadratic equation

y=x²

cubic

y=x³

square root/radical equation

y=√x

inverse/rational equation

y=1/x

absolute value equation

y=|x|

sine equation

y=sinx

f(x)+c

up “c” units

f(x)-c

down “c” units

f(x+c)

left “c” units

f(x-c)

right “c” units

-f(x)

reflects over x axis

f(-x)

reflects over y axis

cf(x) when 0<c<1

vertical shrink

cf(x) when c>1

vertical stretch

f(cx) when 0<c<1

horizontal stretch

f(cx) when c>1

horizontal shrink

does horizontal stretch stretch out or compact the graph?

stretches out

does horizontal shrink stretch out or compact the graph?

compacts the graph

what key feature is this?

y-intercepts

what key feature is this?

x-intercepts

what key feature is this?

maximum

what key feature is this?

minimum

what key feature is this? (first half of the graph)

increasing

what key feature is this? (second half of the graph)

decreasing

what key feature is this?

asymptote

what type of graph is this?

linear

what type of graph is this?

exponential

what type of graph is this?

quadratic

what type of graph is this?

cubic

what type of graph is this?

square root/radical

what type of graph is this?

inverse/rational

what type of graph is this?

absolute value

what type of graph is this?

sine