2.6 Transformation of Functions

y=f(x)+c

y=f(x)+c

Shift the graph of y=f(x) upward c units

y=f(x)-c

Shift the graph of y=f(x) downward c units

y=f(x-c)

Shift the graph of y=f(x) right c units

y=f(x+c)

Shift the graph of y=f(x) left c units

y=-f(x)

Reflect the graph of y=f(x) in the x-axis

y=f(-x)

Reflect the graph of y=f(x) in the y-axis

y=cf(x)

Stretch or shrink the graph of y=f(x) vertically by a factor of c

y=f(cx)

Shrink or stretch the graph of y=f(x) horizontally by a factor of 1/c

Even

Let f be a function, f is _____ if f(-x)=f(x) for all x in the domain of f

Odd

Let f be a function, f is _____ if f(-x)=-f(x) for all x in the domain of f