Question 1012214

{{{f(x)=x}}},are described below.

•Reflection over the {{{x}}} axis:

-f (x) reflects f (x) over the x-axis

{{{highlight(f(x)=-x)}}}->Our new line has negative slope.


•Vertical compression by a scale factor of {{{0.5}}}:

f (ax) stretches/compresses f (x) horizontally

    if 0 < a < 1 (a fraction), the graph is stretched horizontally by a factor
    of a units.

    if a > 1, the graph is compressed horizontally by a factor of a units.
    if a should be negative, the horizontal compression or horizontal stretching of the graph is followed by a reflection of the graph across the y-axis.

a f (x) stretches/compresses f (x) vertically


    if 0 < a < 1 (a fraction), the graph is compressed vertically by a factor
    of a units.
    if a > 1, the graph is stretched vertically by a factor of a units.
If a should be negative, then the vertical compression or vertical stretching of the graph is followed by a reflection across the x-axis.
 

{{{highlight(f(x)=-(0.5x))}}}

•Horizontal shift of {{{4}}} units to the right:
f (x + a) translates f (x) horizontally

    if a > 0, the graph translates (slides) to the right.
    if a < 0, the graph translates (slides) to the left.

{{{highlight(f(x)=-0.5(x+4))}}}

•Vertical shift of {{{3}}} units down:

f (x)+ a  translates f (x) vertically

    if a > 0, the graph translates (slides) upward.
    if a < 0, the graph translates (slides)
    downward.

{{{highlight(f(x)=-0.5(x+4)-3)}}}


{{{ graph( 600, 600, -10, 10, -10, 10, x, -0.5(x+4)-3) }}}