1. The function f has symmetry with respect to the y-axis
2. The function f has symmetry with respect to the origin.
3. The function f has symmetry with respect to the x-axis.

6.  Suppose the graph of f is given. Describe how the graph of each function can be obtained from the graph of f. 

(a)    f(x + 7)

1. shift left 7 units
2. shift right 7 units
3. shift up 7 units
4. shift down 7 units
5. stretch vertically by a factor of 7

(b)    f(x) + 4

1. shift left 4 units
2. shift right 4 units
3. shift up 4 units
4. shift down 4 units
5. stretch vertically by a factor of 4

7. Suppose the graph of f is given. Describe how the graph of each function can be obtained from the graph of f.

1. shift 2 units to the right and 4 units upward
2. shift 4 units to the right and 2 units upward
3. shift 2 units to the right and 4 units downward
4. shift 4 units to the left and 2 units upward
5. shift 4 units to the left and 2 units downward

1. shift 5 units to the right and 3 units upward
2. shift 3 units to the right and 5 units downward
3. shift 3 units to the left and 5 units upward
4. shift 5 units to the right and 3 units downward
5. shift 5 units to the left and 3 units downward

8. Suppose the graph of f is given. Describe how the graph of each function can be obtained from the graph of f.

(a)   1 − f(−x)

1. shift 1 unit upward
2. reflect about the x-axis, then reflect about the y-axis and shift 1 unit downward  
3. reflect about the y-axis and shift 1 unit upward
4. reflect about the x-axis and shift 1 unit upward
5. reflect about the x-axis, then reflect about the y-axis and shift 1 unit upward

(b)    7 − 

1. shrink vertically by 1/6, then reflect about the x-axis and shift 7 units downward
2. stretch vertically by 1/6, then reflect about the x-axis and shift 7 units upward 
3. stretch vertically by 1/6, then reflect about the x-axis and shift 7 units downward
4. shrink vertically by 1/6, then reflect about the y-axis and shift 7 units upward
5. shrink vertically by 1/6, then reflect about the x-axis and shift 7 units upward

9.  Suppose the graph of f is given. Describe how the graph of each function can be obtained from the graph of f. 

1. shift 4 units to the right, shrink vertically by 1/3, then shift upward 5 units
2. shift 4 units to the right, stretch vertically by 1/3, then shift upward 5 units
3. shift 4 units to the left, stretch vertically by 1/3, then shift upward 5 units
4. shift 4 units to the left, shrink vertically by 1/3, then shift upward 5 units
5. shift 4 units to the right, shrink vertically by 1/3, then shift downward 5 units

(b)    4f(x + 1) + 9

1.  shift 1 unit to the right, stretch vertically by 4, then shift upward 9 units
2. shift 1 unit to the right, shrink vertically by 4, then shift upward 9 units
3. shift 1 unit to the left, stretch vertically by 4, then shift downward 9 units
4. shift 1 unit to the left, stretch vertically by 4, then shift upward 9 units
5. shift 1 unit to the left, shrink vertically by 4, then shift upward 9 units

10. Suppose the graph of f is given. Describe how the graph of each function can be obtained from the graph of f.

1.  shrink vertically by a factor of
   $\frac{1}{7}$

   , then shift up 6 units

2. stretch vertically by a factor of 7, then shift up 6 units
3. shrink horizontally by a factor of
   $\frac{1}{7}$

   , then shift down 6 units

4. shrink horizontally by a factor of
   $\frac{1}{7}$

   , then shift right 6 units

5. stretch horizontally by a factor of 7, then shift down 6 units

(b)    y = 7f

11. A function f is given, and the indicated transformation is applied to its graph. Write the equation for the final transformed graph.

f(x) = x²; shift downward 6 units

y =

12.  A function f is given, and the indicated transformation is applied to its graph. Write the equation for the final transformed graph.

f(x) = 

;  shift 7 units to the left

13.  A function f is given, and the indicated transformations are applied to its graph (in the given order). Write the equation for the final transformed graph.

f(x) = |x|; shift 6 units to the left and shift downward 7 units

y= 

14.  A function f is given, and the indicated transformations are applied to its graph (in the given order). Write the equation for the final transformed graph.

f(x) = |x|; reflect in the x-axis, shift 3 units to the right, and shift upward 6 units

15.  A function f is given, and the indicated transformations are applied to its graph (in the given order). Write the equation for the final transformed graph.

f(x) = x²; stretch vertically by a factor of 5, shift downward 4 units, and shift 7 units to the right

 16. The graphs of f and g are given. Find a formula for the function g. 

$g\left(x\right)$

= 

17. The graphs of f and g are given. Find a formula for the function g.

$g\left(x\right) =$

18.  The graphs of f and g are given. Find a formula for the function g. 

$g\left(x\right) =$