4.3E: Exercises - Understanding Transformations of Functions
( \newcommand{\kernel}{\mathrm{null}\,}\)
Exercise 4.3E.1
Match the graph to the function definition.






- f(x)=√x+4
- f(x)=|x−2|−2
- f(x)=√x+1−1
- f(x)=|x−2|+1
- f(x)=√x+4+1
- f(x)=|x+2|−2
- Answer
-
1. e
3. d
5. f
Exercise 4.3E.2
Graph the given function. Identify the basic function and translations used to sketch the graph. Then state the domain and range.
- g(x)=−4
- g(x)=2
- f(x)=x+3
- f(x)=x−2
- g(x)=x2+1
- g(x)=x2−4
- g(x)=(x−5)2+2
- g(x)=(x+2)2−5
- h(x)=|x−1|−3
- h(x)=|x+2|−5
- g(x)=√x−2+1
- g(x)=√x+2+3
- h(x)=(x−1)3−4
- h(x)=(x+1)3+3
- f(x)=1x+1−2
- f(x)=1x−3+3
- f(x)=3√x−2+6
- f(x)=3√x+8−4
- Answer
-
1. Basic graph y=−4; domain: (−∞,∞); range: {−4}
Figure 2.5.37 3. y=x; Shift up 3 units; domain: (−∞,∞); range: (−∞,∞)
Figure 2.5.24 5. y=x2; Shift up 1 unit; domain: (−∞,∞); range: [1,∞)
Figure 2.5.25 7. y=x2; Shift right 5 units and up 2 units; domain: (−∞,∞); range: [2,∞)
Figure 2.5.27 9. y=|x|; Shift right 1 unit and down 3 units; domain: (−∞,∞); range: [−3,∞)
Figure 2.5.29 11. y=√x; Shift right 2 units and up 1 unit; domain: [2,∞); range: [1,∞)
Figure 2.5.31 13. y=x3; Shift right 1 unit and down 4 units; domain: (−∞,∞); range: (−∞,∞)
Figure 2.5.33 15. y=1x; Shift left 1 unit and down 2 units; domain: (−∞,−1)∪(−1,∞); range: (−∞,−2)∪(−2,∞)
Figure 2.5.36 17. y=3√x; Shift up 6 units and right 2 units; domain: (−∞,∞); range: (−∞,∞)
Figure 2.5.38
Exercise 4.3E.3
Graph the piecewise functions.
- h(x)={x2+2 if x<0x+2 if x≥0
- h(x)={x2−3 if x<0√x−3 if x≥0
- h(x)={x3−1 if x<0|x−3|−4 if x≥0
- h(x)={x3 if x<0(x−1)2−1 if x≥0
- Answer
-
1.
Figure 2.5.39 3.
Figure 2.5.40
Exercise 4.3E.4
Write an equation that represents the function whose graph is given.
1.

2.

3.

4.

5.

6.

7.

8.

- Answer
-
1. f(x)=√x−5
3. f(x)=(x−15)2−10
5. f(x)=1x+8+4
7. f(x)=√x+16−4
Exercise 4.3E.5
Match the graph to the given function definition.






- f(x)=−3|x|
- f(x)=−(x+3)2−1
- f(x)=−|x+1|+2
- f(x)=−x2+1
- f(x)=−13|x|
- f(x)=−(x−2)2+2
- Answer
-
1. b
3. d
5. f
Exercise 4.3E.6
Use the transformations to graph the following functions.
- f(x)=−x+5
- f(x)=−|x|−3
- g(x)=−|x−1|
- f(x)=−(x+2)2
- h(x)=√−x+2
- h(x)=−√x−2+1
- g(x)=−x3+4
- f(x)=−x2+6
- Answer
-
1.
Figure 2.5.57 3.
Figure 2.5.58 5.
Figure 2.5.59 7.
Figure 2.5.61