Due: 28 October 2011
Math 1090-002
22 October 2011
Section 3.6 Homework
Instructions: Complete the following problems in the space provided. Please
show your work; write down enough so that a classmate could follow the steps
you’ve taken to arrive at the solution. Each problem is worth 3 points, and you
can earn up to 25 points on the assignment.
The absolute value function is defined as
(
f (x) = |x| =
−x
if x < 0
x
if x ≥ 0
For example,
f (0) = |0| = 0,
f (1) = |1| = 1,
f (−1) = | − 1| = 1,
f (2) = |2| = 2,
f (−2) = | − 2| = 2,
and so on.
The absolute value functions gives the distance of a number x from 0.
1
The plot of this function is given below:
The following functions are transformed versions of the base function
y = f (x) = |x|.
For each function, describe all transformations, and then draw the graph of the
function on the axes provided.
2
1. y = g(x) = −|x|.
(a) Vertical and/or horizontal shift? By how much? In which direction(s) (i.e.
up or down, left or right)?
(b) Vertical and/or horizontal reflection?
(c) Vertical deformation (stretch or shrink)? By what factor?
(d) Horizontal deformation (stretch or shrink)? By what factor?
(e) Plot the function.
3
2. y = g(x) = | − x| + 3.
(a) Vertical and/or horizontal shift? By how much? In which direction(s)?
(b) Vertical and/or horizontal reflection?
(c) Vertical deformation (stretch or shrink)? By what factor?
(d) Horizontal deformation (stretch or shrink)? By what factor?
(e) Plot the function.
4
3. y = g(x) = |2(x − 1)|.
(a) Vertical and/or horizontal shift? By how much? In which direction(s)?
(b) Vertical and/or horizontal reflection?
(c) Vertical deformation (stretch or shrink)? By what factor?
(d) Horizontal deformation (stretch or shrink)? By what factor?
(e) Plot the function.
5
4. y = g(x) = −3| 12 (x + 1)| − 4.
(a) Vertical and/or horizontal shift? By how much? In which direction(s)?
(b) Vertical and/or horizontal reflection?
(c) Vertical deformation (stretch or shrink)? By what factor?
(d) Horizontal deformation (stretch or shrink)? By what factor?
(e) Plot the function.
6
The square root function is defined as
y = f (x) =
For example,
f (0) =
f (1) =
f (4) =
f (9) =
√
√
√
√
0 = 0,
1 = 1,
4 = 2,
9 = 3,
and so on.
The plot of this function is given below:
7
√
x.
The following functions are transformed versions of the base function
y = f (x) =
√
x.
For each function, describe all transformations, and then draw the graph of the
function on the axes provided.
8
√
5. y = g(x) = − x − 4.
(a) Vertical and/or horizontal shift? By how much? In which direction(s)?
(b) Vertical and/or horizontal reflection?
(c) Vertical deformation (stretch or shrink)? By what factor?
(d) Horizontal deformation (stretch or shrink)? By what factor?
(e) Plot the function.
9
6. y = g(x) =
√
−x + 5.
(a) Vertical and/or horizontal shift? By how much? In which direction(s)?
(b) Vertical and/or horizontal reflection?
(c) Vertical deformation (stretch or shrink)? By what factor?
(d) Horizontal deformation (stretch or shrink)? By what factor?
(e) Plot the function.
10
7. y = g(x) =
√
2x.
(a) Vertical and/or horizontal shift? By how much? In which direction(s)?
(b) Vertical and/or horizontal reflection?
(c) Vertical deformation (stretch or shrink)? By what factor?
(d) Horizontal deformation (stretch or shrink)? By what factor?
(e) Plot the function.
11
√
8. y = g(x) = 4 −x − 1 − 3.
(a) Vertical and/or horizontal shift? By how much? In which direction(s)?
(b) Vertical and/or horizontal reflection?
(c) Vertical deformation (stretch or shrink)? By what factor?
(d) Horizontal deformation (stretch or shrink)? By what factor?
(e) Plot the function.
12