harder graphs: graph transformations

translation c units up

y = f(x)+c

translation d units to the right

y = f(x-d)

vertical stretch with scale factor p

y = pf(x)

horizontal stretch with scale factor q

y = f(1/q x)

reflection in the x-axis (vertical reflection)

y = -f(x)

reflection in the y-axis (horizontal reflection)

y = f(-x)

in a horizontal translation, what stays the same?

y values

in a vertical translation, what stays the same?

x values

in a horizontal stretch, what stays the same?

y values

in a vertical stretch, what stays the same?

x values

what does a positive cubic graph look like?

what does a negative cubic graph look like?

what does a positive reciprocal graph look like?

a/x

what does a positive exponential graph where a>1 look like?

a^x

what does a negative exponential graph look like where a>1?

a^(-x)

why does the line not touch 0 on the x-axis for a reciprocal or exponential graph?

k>0 and x>0

what is the equation for a circle on a graph?

x² + y² = r²

e.g. x² + y² = 49

what is the period of a cosine or sine graph?

360

what is the period of a tangent graph?

180

at which points does a cosine graph touch the x-axis?

90, 270, 450

at which points does a sine graph touch the x-axis?

0, 180, 360

at which points does a tangent graph touch the x-axis?

0, 180, 360

where are the asymptotes on a tangent graph?

90, 270

what does a positive exponential graph look like where 0<a<1?

same as a negative exponential graph where a>1

(combination graph) what does the graph a/x² look like?

reciprocal + quadratic

(combination graph) what does the graph -a/x² look like?

negative reciprocal + quadratic