Question

GAIN A MEDAL AND A FAN

Part a: write the function rule for each function reflected in the given axis
f(x) = x+1 ; x axis

f(x) = 3x ; x axis

f(x) = 2x - 4 ; x axis


Part b: Write an equation for each transformation of y=x

Vertical stretch by a factor of 4

vertical stretch by a factor of 2

vertical compression by a factor of 1/2

vertical compression by a factor of 1/4

Answer 1

to reflect about the x axis, find -f(x).

Answer 2

\[g(x) = a\cdot f \left(x-h \right)+k\]

where a is a vertical stretch if |a|>1 and vertical compression if 0<|a|<1
a reflection about the x axis if a < 0 (i.e. if a is negative)

a horizontal shift of h and a vertical shift of k.

remember for the horizontal shift, h is the value of x which make (x-h) = 0