1314 2.5 Transformations of Functions

y=cf(x), c>1

multiply each y-coordinate of y=f(x) by c, vertically stretching the graph of f

y=-f(x)

reflection over x-axis

y=f(-x)

reflection over y-axis

y=f(x)-c

vertical shift down

y=f(x)+c

vertical shift up

Suppose that the graph of a function g is known. The graph of y=g(x)+2 may be obtained by a ____ shift of the graph of g ___ a distance.

vertical, up

The graph of y=2f(x) is obtained by a _____ stretch of the graph of y=f(x) by multiplying each of its ____ coordinates by 2.

vertical, y

The graph of y=-f(x) is the graph of y=f(x) reflected about the _____.

x-axis

Suppose that the graph of a function f is known. Then the graph of y=f(-x) may be obtained by a reflection about the _____ of the graph of the function y=f(x).

y-axis

Graph the absolute value function, f(x)=|x| then graph g(x)=-4|x+1|-5

1) horizontal shift 1 to the L / horizontal translation 2) graph is stretched by a factor of 4 V-v 3) somewhere it's multiplied by -1, flip 4) shift vertically down 5

Graph the absolute value function of f(x)=|x|, then use transformations to graph h(x)=|x-3|-6

1) horizontal shift R 3 units/ horizontal translation 2) no horizontal stretch/ shrink (coefficient of x is 1) 3) no reflection, no negative in front of equation 4) vertical downshift of 6 / vertical translation

Use the transformations fo the graph f(x)=x^3 to graph h(x)=-(x-2)^3

1) horizontal shift to the R 2 units 2) no horizontal/ vertical stretch 3) the - sign means it is flipped/ reflected about the x-axis

Use transformation of f(x)=x^2 to graph function g(x)=2(x-1)^2+1

1) horizontal shift to the R by 1 unit (+1) 2) graph is stretched by 2 vertically 3) no reflection because graph is not multiplied by -1 4) vertical shift of 1 unit up

Use transformations fo f(x)=^3square root x to graph h(x)=^3square root x-5

1) shifts horizontally R 5 units 2) not multiplied by a constant 1 or -1, no stretch/ shrink 3) is being multiplied by a -1 will reflect about the x-axis 4) no vertical shift

Graph f(x)=square root x then graph h(x)=-sq. root x+6

1) the +6 gives it a shift of 6 units to the L 2) the - sign in front of the square root means it's flipped

y=f(cx), c>1

Divide each x-coordinate of y=f(x) by c, horizontally shrinking the graph of f.

y=f(cx), 0<c<1

Divide each x-coordinate of y=f(x) by c, horizontally stretching the graph of f.

To obtain the graph of f(x)=sq. root of x+2, shift the graph of y=sq. root of x horizontally to the right 2 units.

False

Order of Transformations 1:

Horizontal Shifting

y=cf(x),0<c<1

Multiply each y-coordinate of y=f(x) by c, vertically shrinking the graph of f

Order of Transformations 3:

Reflecting

Order of Transformations 2:

Stretching or Shrinking

Order of Transformations 4:

Vertical Shifting

Morphing

a character or object having one shape becoming transformed in a fluid fashion into a quite different shape

y=f(x+c)

horizontal shift left

y=f(x-c)

horizontal shift right

Suppose that the graph of a function is known. Then the graph of y=f(x-2) may be obtained by a _____ shift of the graph of f to the ____ a distance of 2 units.

horizontal, right