Math 2B/3A Name: Answer Key . Review of Function...
5
Math 2B/3A Name: Answer Key . Review of Function Transformations Block: B or F 25 October 2013 We have been using several basic functions in this unit and you need to be familiar enough with them that you can sketch them quickly and accurately. For each of the following: a. Make a sketch that shows the general shape (no accuracy required) b. Make a short table of values c. Make a more accurate graph using your table of values. How did you do on your shape sketch? d. Label your graph with the “name” of the function from the word bank: 1. y = x 2 quadratic 2. y = | x | absolute value Linear Quadratic Cubic Square Root Exponential Absolute Value Circle x y –3 9 –2 4 –1 1 0 0 1 1 2 4 3 9 x y –3 3 –2 2 –1 1 0 0 1 1 2 2 3 3
Transcript of Math 2B/3A Name: Answer Key . Review of Function...
Math 2B/3A Name: Answer Key . Review of Function Transformations Block: B or F 25 October 2013 We have been using several basic functions in this unit and you need to be familiar enough with them that you can sketch them quickly and accurately. For each of the following:
a. Make a sketch that shows the general shape (no accuracy required) b. Make a short table of values c. Make a more accurate graph using your table of values. How did you do
on your shape sketch? d. Label your graph with the “name” of the function from the word bank:
1. y = x2 quadratic 2. y = | x | absolute value
Linear Quadratic Cubic Square Root Exponential Absolute Value Circle
x y
–3 9
–2 4
–1 1
0 0
1 1
2 4
3 9
x y
–3 3
–2 2
–1 1
0 0
1 1
2 2
3 3
Review for Function Transformation Quiz page 2
y = x linear 3. y =
€
x square root 4. y = x3 cubic
x y
–3 –3
–2 –2
–1 –1
0 0
1 1
2 2
3 3
x y
–1 –
0 0
1 1
4 2
9 3
16 4
25 5
x y
–3 –27
–2 –8
–1 –1
0 0
1 1
2 8
3 27
Review for Function Transformation Quiz page 3
x2 + y2 = 1 circle 5. y = 2x exponential 8. We also looked at what different changes to the equation do to the graph. Fill in the table of
transformations below:
y = f(x + h) left h y = f(ax) 1/a as wide y = f(–x) flip over y-axis
y = f(x – h) right h
€
y = f xa⎛
⎝ ⎜ ⎞
⎠ ⎟ a times as wide
y + k = f(x) down k by = f(x) 1/b as tall –y = f(x) flip over x-axis
y – k = f(x) up k
€
yb
= f (x) b times as tall
x y
–1 0
–3/5 4/5
0 1
3/5 4/5
1 0
3/5 –4/5
0 –1
x y
–3 1/8
–2 ¼
–1 ½
0 1
1 2
2 4
3 8
Review for Function Transformation Quiz page 4
9. For each of the following: • Describe the transformation • Sketch the transformed basic function (the grid means you should be reasonably accurate)
a. y = (x – 5)2 right 5 b. 2y = | x | half as tall c. y – 1 =
€
x + 3 up 1, left 3
d. y + 2 = (–x)3 down 2, flip over y e. 3y = 5x 1/3 as tall, 1/5 as wide f.
€
−y = 2−x flip over x, flip over y
g.
€
x2⎛
⎝ ⎜ ⎞
⎠ ⎟ 2
+y4⎛
⎝ ⎜ ⎞
⎠ ⎟ 2
=1 twice as wide h. (x + 3)2 + (y – 2)2 = 4 left 3 i.
€
x + 3( )2 +y4⎛
⎝ ⎜ ⎞
⎠ ⎟ 2
=1 left 3
4 times as tall up 2 4 times as tall
10
5
–5
–10
–10 10
10
5
–5
–10
–10 10
10
5
–5
–10
–10 10
–10 10
10
5
–5
–10
–10 10
10
5
–5
–10
–10 10
10
5
–5
–10
–10 10
10
5
–5
–10
–10 10
10
5
–5
–10
–10 10
10
5
–5
–10
Review for Function Transformation Quiz page 5
10. Write the equations of the transformed functions shown below. Remember, it often helps to write
the basic function and what the transformations are before you try to write the equation.
a. b. Circle: x2 + y2 = r2, right 1, up 3, radius 4 Square root: flip over y-axis, down 5 (x – 1)2 + (y – 3)2 = 16
€
y + 5 = −x
c. d. Exponential: y = 2x, flip over x-axis, half as tall Cubic: left 4, down 2 –2y = 2x y + 2 = (x + 4)3
