Parent Functions for Math MA

What function is this?

y=mx+b

What function is this?

y=x²

What function is this?

y=x³

What function is this?

y=the square root of x

What function is this?

y=|x|

What function is this?

y=1/x

What function is this?

y=1/x²

Average speed equals:

distance/time

Average velocity equals:

change in position/time elapsed

-f(x)

reflection over x-axis

f(-x)

reflection over y-axis

f(x)+k

vertical shift

f(x+k)

horizontal shift

|f(x)|

leave positive values alone, reflect everything else over x

kf(x)

vertical shift or compression

f(kx)

horizontal stretch or compression

for vertical stretches or compressions if a > 1

it’s a vertical stretch

for vertical stretches or compressions if 0 < |a| < 1

it’s a vertical compression

for horizontal stretches or compressions if |b| > 1

it’s a horizontal compression

for horizontal stretches or compressions if 0 < |b| < 1

it’s a horizontal stretch