Question

hi! number one and number two are causing me trouble, so if anyone would like to answer either that’d be appreciated. thanks in advance:)

Answer 1

• 
  `√(x - 5) + 4`
• 
  `3 √(x + 3) + 2`
• 
  `- √(x + 2) - 2`
• 
  `- 2 √(x) + 3`
• Type these function in for 1a,1b,2a,2b respectively and look for table of values

Explanation:

1a) The function will shift 5 units to the right, 4 units down,

1b).The function will shift 3 units to the left, stretched in the y direction by a scale factor of 3, and shift up 2 units.

2a). The function will shift 2 units to the left, reflect over the x axis, and shift 2 units down.

2b) The function will stretched in the y direction by a scale factor of -2 and shift the function up 3 units.

Answer 2

9514 1404 393

Answer:

1a. translation right 5, down 4

1b. vertical stretch ×3, translation left 3, up 2

2a. translation left 2, down 2

2b. reflect in x, vertical stretch ×2, translation up 3

3. f(x) = -4/(x+5)+4

4. f(x) = 1/2√(3(x +3)) -4

Explanation:

Transformations of functions can be decoded by considering the transformation ...

g(x) = a·f((x-h)/b) +k

The transformations here are ...

• vertical stretch by a factor of 'a'
• horizontal stretch by a factor of 'b'
• right shift by h units
• up shift by k units

Note that either 'a' or 'b' can be a fraction less than 1, which results in a transformation usually described as a compression (not a stretch). If either of these is negative, then a reflection over the x-axis (a<0) or y-axis (b<0) is also involved. The stretch (or compression) and/or reflection is applied before the translation the way this is written.

_____

1a. translation right 5, down 4

1b. vertical stretch by a factor of 3, translation left 3, up 2

__

2a. translation left 2, down 2

2b. reflected across the x-axis, vertically stretched by a factor of 2, translated up 3

__

3. a=4, b=-1, h=-5, k=4

f(x) = -4/(x+5)+4

__

4. a=1/2, b=1/3, h=-3, k=-4

f(x) = 1/2√(3(x +3)) -4

_____

The graphs in the attachments show the various functions. (It takes a little work to verify that the graph in the last attachment has the appropriate compressions, but it does.)